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# (Solved) MATH225 Week 4 Assignment Probability Terminology and Notation

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Question

A survey was conducted to see whether age has an association with the belief that a master’s degree or higher provides an advantage in one’s career. Of the 524 adults between the ages of 22 and 25 surveyed, 56% believed that a master’s degree has value in a person’s career path. Of the 458 adults surveyed between the ages of 40 and 45, 52% also believed that a master’s degree has value in a person’s career path. Assuming age is not associated with this belief, the probability of the data being the result of chance is calculated to be 0.21. Interpret this calculation.

• We can expect 56% of all adults between the ages of 22 and 25 to believe a master’s degree or higher provides an advantage in one’s career.
• The data is statistically significant at the 0.05 level of significance in showing that age has an association with the belief that a master’s degree or higher provides an advantage in one’s career.
• Age does not have any association with the belief that a master’s degree or higher provides an advantage in one’s career.
• The data are not statistically significant at the 0.05 level of significance in showing that age has an association with the belief that a master’s degree or higher provides an advantage in one’s career.

Question

A recent study was conducted to determine the concentration of lead in drinking water across various states. 25 water samples from the state of Washington were tested; the mean lead concentration was found to be 0.15%. This compares to 32 water samples in the state of Minnesota where the mean was reported to be 0.21%. The data was calculated to be significant at the 0.0001 level. Determine the meaning of this significance level.

• At the 0.0001 level of significance, the concentration of lead is higher in water from Minnesota.
• It is not unusual to see a 0.15% concentration of lead in drinking water because lead in drinking water is highly regulated.
• We can expect that any 32 water samples from Minnesota will have an average lead concentration of 0.21%.
• It is certain that drinking water in Minnesota has a higher lead concentration than drinking water in Washington.

Question

Which of the following gives the definition of trial?

• a particular result of an experiment
• one specific execution of an experiment
• a planned activity carried out under controlled conditions
• the set of all possible outcomes of an experiment

Question

The mean body temperature of a human is accepted to be 98.6∘F. In a study, the body temperatures of 127 individuals were measured. The mean body temperature of the individuals was calculated to be 99.0∘F. Assuming the regular body temperature of humans is actually 98.6∘F, the probability of these results occurring by chance is less than 0.01. Interpret the results of the calculation.

• We can expect that the mean body temperature of any 127 individuals is 99.0∘F.
• The mean body temperature of humans is not 98.6∘F.
• At the 0.01 level of significance, the mean body temperature of humans is not 98.6∘F.
• Since human body temperature varies, the results of this study are not unusual.

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Question

A farmer claims that the average mass of an apple grown in his orchard is 100g. To test this claim, he measures the mass of 150 apples that are grown in his orchard and determines the average mass per apple to be 98g. The results are calculated to be statistically significant at the 0.01 level. What is the correct interpretation of this calculation?

• The data are not statistically significant at the 0.05 level.
• The mean mass of any 150 apples grown in the farmer’s orchard is 98g.
• At the 0.01 level of significance, the mean mass of the apples grown in the farmer’s orchard is different from 100g.
• At the 0.01 level of significance, the mean mass of the apples grown in the farmer’s orchard is 98g.

Question

Trial best fits which of the following descriptions?

• a particular result of an experiment
• a subset of the set of all outcomes of an experiment
• one repetition or instance of an experiment
• the set of all possible outcomes of an experiment

Question

Patricia will draw 8 cards from a standard 52-card deck with replacement. Which of the following are not events in this experiment?

Select all that apply:

• drawing 8 hearts
• drawing 8 cards
• drawing 1 card
• drawing 3 kings

Question

A hospital takes record of any birth that occurs there every day. On one day, the hospital reports that 35 of the 62 babies born were girls. Assuming that all of the parents did not have any gender selection procedures, there is a probability of 0.31 of getting these results by chance. Do these results have statistical significance at the 0.05 level of significance?

• Yes, the probability of the results occurring is less than 0.05.
• No, the probability of the results occurring is less than 0.05.
• Yes, the probability of the results occurring is greater than 0.05.
• No, the probability of the results occurring is greater than 0.05.

Question

A standard roulette wheel with slots labeled 0, 00, 1, 2, 3, … , 36 is spun 60 times. Of these spins, the number 7 is spun 7 times. Assuming the wheel is fair, the probability of this occurring by chance is 0.00001. Do these results have statistical significance at the 0.01 level of significance?

• No, the probability of the results occurring is greater than 0.01.
• Yes, the probability of the results occurring is less than 0.01.
• No, the probability of the results occurring is less than 0.01.
• Yes, the probability of the results occurring is greater than 0.01.

Question

Paul will roll two standard dice simultaneously. If Event A = both dice are odd and Event B = at least one die is even, which of the following best describes events A and B?

Select all that apply:

• Mutually Exclusive
• Not mutually exclusive
• Independent
• Dependent

Question

Arianna will roll a standard die 10 times in which she will record the value of each roll. What is a trial of this experiment?