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(Solved) MATH225 Week 8 Final Exam

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QUESTION 1

A fitness center claims that the mean amount of time that a person spends at the gym per visit isÂ 33Â minutes. Identify the null hypothesis,Â H0, and the alternative hypothesis,Â Ha, in terms of the parameterÂ Î¼.

• H0:Â Î¼â‰ 33;Â Ha:Â Î¼=33
• H0:Â Î¼=33;Â Ha:Â Î¼â‰ 33
• H0:Â Î¼â‰¥33;Â Ha:Â Î¼<33
• H0:Â Î¼â‰¤33;Â Ha:Â Î¼>33

QUESTION 2

The answer choices below represent different hypothesis tests. Which of the choices areÂ right-tailedÂ tests? Select all correct answers.

Select all that apply:

• H0:Xâ‰¥17.1, Ha:X<17.1
• H0:X=14.4, Ha:Xâ‰ 14.4
• H0:Xâ‰¤3.8,Â Ha:X>3.8
• H0:Xâ‰¤7.4,Â Ha:X>7.4
• H0:X=3.3, Ha:Xâ‰ 3.3

QUESTION 3

Find the Type II error given that the null hypothesis,Â H0, is: a building inspector claims that no more thanÂ 15%Â of structures in the county were built without permits.

• The building inspector thinks that no more thanÂ 15%Â of the structures in the county were built without permits when, in fact, no more thanÂ 15%Â of the structures really were built without permits.
• The building inspector thinks that more thanÂ 15%Â of the structures in the county were built without permits when, in fact, more thanÂ 15%Â of the structures really were built without permits.
• The building inspector thinks that more thanÂ 15%Â of the structures in the county were built without permits when, in fact, at mostÂ 15%Â of the structures were built without permits.
• The building inspector thinks that no more thanÂ 15%Â of the structures in the county were built without permits when, in fact, more thanÂ 15%Â of the structures were built without permits.

QUESTION 4

Suppose a chef claims that her meatball weight is less thanÂ 4Â ounces, on average. Several of her customers do not believe her, so the chef decides to do a hypothesis test, at aÂ 10%Â significance level, to persuade them. She cooksÂ 14Â meatballs. The mean weight of the sample meatballs isÂ 3.7Â ounces. The chef knows from experience that the standard deviation for her meatball weight isÂ 0.5Â ounces.

• H0:Â Î¼â‰¥4;Â Ha:Â Î¼<4
• Î±=0.1(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

QUESTION 5

What is theÂ p-value of aÂ right-tailedÂ one-mean hypothesis test, with a test statistic ofÂ z0=1.74? (Do not round your answer; compute your answer using a value from the table below.)

QUESTION 6

Kenneth, a competitor in cup stacking, claims that his average stacking time isÂ 8.2Â seconds. During a practice session, Kenneth has a sample stacking time mean ofÂ 7.8Â seconds based onÂ 11Â trials. At theÂ 4%Â significance level, does the data provide sufficient evidence to conclude that Kenneth’s mean stacking time is less thanÂ 8.2Â seconds? Accept or reject the hypothesis given the sample data below.

• H0:Î¼=8.2Â seconds;Â Ha:Î¼<8.2Â seconds
• Î±=0.04(significance level)
• z0=âˆ’1.75
• p=0.0401

• Do not reject the null hypothesis because theÂ p-valueÂ 0.0401Â is greater than the significance levelÂ Î±=0.04.
• Reject the null hypothesis because theÂ p-valueÂ 0.0401Â is greater than the significance levelÂ Î±=0.04.
• Reject the null hypothesis because the value ofÂ zÂ is negative.
• Reject the null hypothesis becauseÂ |âˆ’1.75|>0.04.
• Do not reject the null hypothesis becauseÂ |âˆ’1.75|>0.04.

QUESTION 7

A recent study suggested thatÂ 81%Â of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selectsÂ 59Â senior citizens patients who were treated at the hospital and finds thatÂ 49Â of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test?

• {H0:p=0.81Ha:p>0.81
• {H0:pâ‰ 0.81Ha:p=0.81
• {H0:p=0.81Ha:p<0.81
• {H0:p=0.81Ha:pâ‰ 0.81

QUESTION 8

A researcher claims that the proportion of cars with manual transmission is less thanÂ 10%. To test this claim, a survey checkedÂ 1000Â randomly selected cars.Â  Of those cars,Â 95Â had a manual transmission.

The following is the setup for the hypothesis test:

{H0:p=0.10Ha:p<0.10

Find the test statistic for this hypothesis test for a proportion. Round your answer toÂ 2Â decimal places

QUESTION 9

A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. .

The following is the setup for this hypothesis test:

H0:pÂ = 0.12

Ha:pÂ â‰ Â 0.12

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

The following table can be utilized which provides areas under the Standard Normal Curve:

 z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.03 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.04 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068

QUESTION 10

An economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater thanÂ 65%.

To test this claim, a random sample ofÂ 750Â people are asked if they plan to purchase a fully electric vehicle as their next car Â  Of theseÂ 750Â people,Â 513Â indicate that they do plan to purchase an electric vehicle.

The following is the setup for this hypothesis test:

H0:p=0.65

Ha:p>0.65

In this example, the p-value was determined to beÂ 0.026.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level ofÂ 5%.)

• The decision is to reject the Null Hypothesis.
The conclusion is that there is enough evidence to support the claim.
• The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.

QUESTION 11

Becky’s statistics teacher was teaching the class how to perform theÂ z-test for a proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocketÂ would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coinÂ 30Â times and got headsÂ 18Â times.

Becky conducts a one-proportionÂ hypothesis testÂ at theÂ 5%Â significance level, to test whether the true proportion of heads is different fromÂ 50%.

Which answer choice shows the correct null and alternative hypotheses for this test?

• H0:p=0.6;Â Ha:p>0.6, which is a right-tailed test.
• H0:p=0.5;Â Ha:p<0.5, which is a left-tailed test.
• H0:p=0.6;Â Ha:pâ‰ 0.6, which is a two-tailed test.
• H0:p=0.5;Â Ha:pâ‰ 0.5, which is a two-tailed test.

Â QUESTION 12

John owns a computer repair service. For each computer, he chargesÂ \$50Â plusÂ \$45Â per hour of work. A linear equation that expresses the total amount of money John earns per computer isÂ y=50+45x. What are the independent and dependent variables? What is theÂ y-intercept and the slope?

• The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.John charges a one-time fee ofÂ \$50Â (this is whenÂ x=0), so theÂ y-intercept isÂ 50. John earnsÂ \$45Â for each hour he works, so the slope isÂ 45.
• The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer.
• John charges a one-time fee ofÂ \$45Â (this is whenÂ x=0), so theÂ y-intercept isÂ 45. John earnsÂ \$50Â for each hour he works, so the slope isÂ 50.
• The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer.
• John charges a one-time fee ofÂ \$50Â (this is whenÂ x=0), so theÂ y-intercept isÂ 50. John earnsÂ \$45Â for each hour he works, so the slope isÂ 45.
• The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.
• John charges a one-time fee ofÂ \$45Â (this is whenÂ x=0), so theÂ y-intercept isÂ 45. John earnsÂ \$50Â for each hour he works, so the slope isÂ 50.

QUESTION 13

Ariana keeps track of the amount of time she studies and the score she gets on her quizzes. The data are shown in the table below. Which of the scatter plots below accurately records the data?

 Hours studying Â Quiz score 1 5 2 5 3 7 4 9 5 9

QUESTION 14

Data is collected on the relationship between time spent playing video games and time spent with family. The data is shown in the table and the line of best fit for the data isÂ y^=âˆ’0.27x+57.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

According to the line of best fit, the predicted number of minutes spent with family for someone who spentÂ 95Â minutes playing video games isÂ 31.85. Is it reasonable to use this line of best fit to make the above prediction?

• The estimate, a predicted time ofÂ Â 31.85Â minutes,Â is unreliable but reasonable.
• The estimate, a predicted time ofÂ Â 31.85Â minutes,Â is both unreliable and unreasonable.
• The estimate, a predicted time ofÂ Â 31.85Â minutes,Â is both reliable and reasonable.
• The estimate, a predicted time ofÂ Â 31.85Â minutes,Â is reliable but unreasonable.

QUESTION 15

Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the yearÂ 2000Â to the yearÂ 2015? Select all that apply.

Select all that apply:

• yË†=38,000+2500x
• yË†=38,000âˆ’3500x
• yË†=âˆ’38,000+2500x
• yË†=38,000âˆ’1500x

QUESTION 16

True or false: The higher the average daily crops harvested, the closer to the peak of harvest it is.

• True
• False

QUESTION 17

An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the color index, orÂ Bâˆ’VÂ index, and distance (in light years) from Earth forÂ 30Â stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter). This then allows the scientist to know the star’s temperature and a negative value means a hot blue star. A light year is the distance light can travel inÂ 1Â year, which is approximatelyÂ 5.9Â trillion miles.Â The data is provided below. Use Excel to calculate the correlation coefficientÂ rÂ between the two data sets, rounding to two decimal places.

QUESTION 18

The weight of a car can influence the mileage that the car can obtain. A random sample ofÂ 20Â carsâ€™ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find theÂ best fit linear regression equation, where weight is the explanatory variable.Â Round the slope and intercept to three decimal places.

QUESTION 19

A farmer divided his piece of land intoÂ 4Â equivalent groups. The quality of the soil is the same across theÂ 4Â groups of land. He planted the same crop in allÂ 4Â groups of landÂ and recorded the yield of the crop in allÂ 4Â groups for aÂ 4Â week period. Is the study observational or experimental? If it is an experiment, what is the controlled factor?

• The study is an observational study.
• The study is an experiment. The controlled factor is theÂ 4Â week observation period.
• The study is an experiment. The controlled factor is the land.
• The study is an experiment. The controlled factor is the growth of the crops.

QUESTION 20

To test the effectiveness of a drug proposed to relieve symptoms of headache, physicians included participants for a study. They gave the drug to one group and a drug with no therapeutic effect to another group. Which group receives the placebo?

• the physicians
• the group that received the drug with no therapeutic effect
• all of the people in the study

QUESTION 21

A doctor notes her patient’s temperature in degrees Fahrenheit every hour to make sure the patient does not get a fever. What is the level of measurement of the data?

• nominal
• ordinal
• interval
• ratio

QUESTION 22

As a member of a marketing team, you have been tasked with determining the number of DVDs that people have rented over the past six months. You sample twenty adults and decide that the best display of data is a frequency table for grouped data. Construct this table using four classes.

15,31,28,19,14,18,28,19,10,19,10,24,14,18,24,27,10,18,16,23

QUESTION 23

The histogram below displays the weights of rainbowÂ troutÂ (in pounds) caught by all visitors at a lake on a Saturday afternoon. According to thisÂ histogram, which range of weights (in pounds) contains the lowest frequency?

QUESTION 24

Describe the shape of the given histogram.

• uniform
• unimodal and symmetric
• unimodal and left-skewed
• unimodal and right-skewed
• bimodal

QUESTION 25

The bar graph below shows the number of boys and girls in different classes.

How many total students are in Ms. James’s class? Do not include the units in your answer.

QUESTION 26

The line graph shown below represents the number of TVs in a houseÂ by square footage (in hundreds of feet). According to the information above, which of the following isÂ an appropriate analysis of square footage and TVs?

• From the data, the number of TVs doubled from a square footage ofÂ 8.5Â andÂ 10.
• From the data, there is a steady decrease in the square footage and number of TVs.
• From the data, there is a steady increase in the square footage and number of TVs.
• From the data, when the square footage is betweenÂ 8.5Â andÂ 10, the number of TVs remains the same.

QUESTION 27

Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below.

16,14,14,21,15

Find the mean boxes sold.

QUESTION 28

Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median.

20,46,19,14,42,26,33

Median =

QUESTION 29

Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears.

3,12,3,11,5,5,3,10,12

Mode =

QUESTION 30

Given the following histogram, decide if the data is skewed or symmetrical.

• Select the correct answer below:
• The data are skewed to the left.
• The data are skewed to the right.
• The data are symmetric.

QUESTION 31

Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?

• A
• B
• C
• D

QUESTION 32

The graph below shows the graphs of several normal distributions, labeledÂ A,Â B, andÂ C, on the same axis. Determine which normal distribution has the smallest standard deviation.

• A
• B
• C

QUESTION 33

Brayden tosses a coinÂ 500Â times. Of thoseÂ 500Â times, he observes headsÂ a total ofÂ 416Â times. Calculations show that the probability of this occurring by chance is less thanÂ 0.01, assuming the coin is fair. Determine the meaning of the significance level.

• We expect thatÂ 416Â of everyÂ 500Â coin tosses will result in heads.
• At theÂ 0.01Â level of significance, the coin is likely not a fair coin.
• There is certainty that the coin is not a fair coin.
• The results are not statistically significant at theÂ 0.05Â level of significance.

QUESTION 34

Is the statement below true or false?

Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs.

• True
• False

QUESTION 35

Of the following pairs of events, which pair has mutually exclusive events?

• rolling a sum greater thanÂ 7Â from two rolls of a standard die and rolling aÂ 4Â for the first throw
• drawing aÂ 2Â and drawing aÂ 4Â with replacement from a standard deck of cards
• rolling a sum ofÂ 9Â from two rolls of a standard die and rolling aÂ 2Â for the first roll
• drawing a red card and then drawing a black card with replacement from a standard deck of cards

QUESTION 36

Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains.

QUESTION 37

A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean scoreÂ out ofÂ 100Â points was aÂ xÂ¯=77, with a margin of error ofÂ 10.

Construct a confidence interval for the mean score (out ofÂ 100Â points) on the final exam.

QUESTION 38

A random sample of adults were asked whether they prefer reading an e-bookÂ over a printed book. The survey resulted in a sample proportion ofÂ pâ€²=0.14, with a sampling standard deviation ofÂ Ïƒpâ€²=0.02, who preferred reading an e-book.

Use the empirical rule to constructÂ aÂ 95%Â confidence interval for the true proportion of adults who prefer e-books.

QUESTION 39

The population standard deviation for the heights of dogs, in inches, in a city isÂ 3.7Â inches. If we want to beÂ 95%Â confident that the sample mean is withinÂ 2Â inches of the true population mean, what is the minimum sample size that can be taken?

z0.10 1.282 z0.05 1.645 z0.025 1.960 z0.01 2.326 z0.005 2.576

Use the table above for theÂ z-score, and be sure to round up to the nearest integer.

QUESTION 40

Which of the following frequency tables showÂ a skewed data set? Select all answers that apply.

Select all that apply:

•  Value Frequency 5 1 6 2 7 10 8 11 9 17 10 17 11 15 12 12 13 7 14 7 15 0 16 1
•  Value Frequency 5 1 6 3 7 8 8 10 9 13 10 26 11 14 12 12 13 8 14 3 15 1 16 1
•  Value Frequency 12 1 13 1 14 3 15 6 16 23 17 29 18 19 19 15 20 3
•  Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 7 2

QUESTION 41

A poll was conducted during the final game of the basketball season to determine whether fans wanted to see the defending champions win the game or the challenging team win the game. From the poll,Â 216Â of theÂ 374Â residents sampled from urban areas want the defending champions to win the game. In more rural areas,Â 304Â of theÂ 466Â residents polled want the defending champions to win the game. Assuming location has nothing to do with team preference, the probability that the data gathered was the result of chance is calculated to beÂ 0.03. What is the correct interpretation of this calculation?

• More people from rural areas want the defending champions to win the game.
• ExactlyÂ 216Â out of everyÂ 374Â urban residents want the defending champions to win the game.
• The results are statistically significant at theÂ 0.05Â level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas.
• The data is not statistically significant at theÂ 0.05Â level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas.

QUESTION 42

In a psychological study aimed at testing a drug that reduces anxiety, the researcher grouped the participants intoÂ 2Â groups and gave the anxiety-reduction pill to one group and an inert pill to another group. Which group receives the placebo?

• the group that received the anxiety-reduction pill
• the psychological study
• all the people in the study
• the group that received the inert pillÂ

QUESTION 43

Which of the following results in the null hypothesisÂ Î¼â‰¥38Â and alternative hypothesisÂ Î¼<38?

• A fitness center claims that the mean amount of time that a person spends at the gym per visit is at mostÂ 38Â minutes.
• A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer thanÂ 38Â minutes.
• A fitness center claims that the mean amount of time that a person spends at the gym per visit isÂ 38Â minutes.
• A fitness center claims that the mean amount of time that a person spends at the gym per visit is more thanÂ 38Â minutes.

QUESTION 44

True or False:Â Â The more shoesÂ a manufacturer makes, the more shoesÂ they sell.

• True
• False

QUESTION 45

Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument.

QUESTION 46

The answer choices below represent different hypothesis tests. Which of the choices areÂ left-tailedÂ tests? Select all correct answers.

Select all that apply:

• H0:X=17.3, Ha:Xâ‰ 17.3
• H0:Xâ‰¥19.7,Â Ha:X<19.7
• H0:Xâ‰¥11.2,Â Ha:X<11.2
• H0:X=13.2, Ha:Xâ‰ 13.2
• H0:X=17.8, Ha:Xâ‰ 17.8

QUESTION 47

Assume the null hypothesis,Â H0, is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario

• Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does.
• Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does not.
• Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does not.
• Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does.

QUESTION 48

Given the plot of normal distributionsÂ AÂ andÂ BÂ below, which of the following statements is true? Select all correct answers.

Select all that apply:

• A has the larger mean.
• B has the larger mean.
• The means of AÂ andÂ BÂ are equal.
• AÂ has the larger standard deviation.
• B has the larger standard deviation.
• The standard deviations of A and B are equal.

QUESTION 49

Hugo averagesÂ 74Â words per minute on a typing test with a standard deviation ofÂ 11Â words per minute. Suppose Hugo’s words per minute on a typing test are normally distributed. LetÂ X=Â the number of words per minute on a typing test. Then,Â Xâˆ¼N(74,11).

Suppose Hugo typesÂ 51Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=51Â is ________. ThisÂ z-score tells you thatÂ x=51Â is ________ standard deviations to the ________ (right/left) of the mean, ________.

Correctly fill in the blanks in the statement above.

• Suppose Hugo typesÂ 51Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=51Â isÂ 2.091. ThisÂ z-score tells you thatÂ x=51Â isÂ 2.091Â standard deviations to theÂ rightÂ of the mean,Â 74.
• Suppose Hugo typesÂ 51Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=51Â isÂ 1.643. ThisÂ z-score tells you thatÂ x=51Â isÂ 1.643Â standard deviations to theÂ rightÂ of the mean,Â 74.
• Suppose Hugo typesÂ 51Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=51Â isÂ âˆ’2.091. ThisÂ z-score tells you thatÂ x=51Â isÂ 2.091Â standard deviations to theÂ leftÂ of the mean,Â 74.
• Suppose Hugo typesÂ 51Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=51Â isÂ âˆ’1.643. ThisÂ z-score tells you thatÂ x=51Â isÂ 1.643Â standard deviations to theÂ leftÂ of the mean,Â 74.

QUESTION 50

The following frequency table summarizes a set of data. What is the five-number summary?

 Value Frequency Â Â 2 4 5 2 9 1 10 1 12 1 13 4 18 3 19 1 22 1 23 1