Mock Exam Review

Milk has a pH of 6.7, which is slightly acidic. Cheese makers add a culture to milk to lower the pH, making it more acidic and turning it into cheese. A manufacturer is experimenting with a new culture that claims to produce a pH of 5.2, which is perfect for cheddar cheese. A set of 50 test batches resulted in an average pH of 5.11. A 1-sample t-test was conducted to investigate whether there is evidence that the mean pH is different from 5.2. The test resulted in a p-value of 0.018. Which of the following is a correct interpretation of the p-value?

• The probability that the true pH is equal to 5.2 is 0.018.

• The probability that the true pH is different from 5.2 is 0.018

• The probability of observing a sample mean of 5.11 or less is 0.018 if the true mean is 5.2.

• The probability of observing a sample mean of 5.11 or more is 0.018 if the true mean is 5.2.

• The probability of observing a sample mean of 5.11 or less, or of 5.29 or more, is 0.018 if the ture mean is 5.2.

In certain regions of the country, elk can cause damage to agricultural crops by walking through the fields. One strategy designed to limit elk from crossing a field is to surround the field with a fence. Some elk, however, will still be able to bypass the fence. For a period of one month, the number of elk found crossing a sample of fields with a fence was recorded and used to construct the 95% confidence interval (2.9, 4.4) for the mean number of elk. Assume that the conditions for inference were checked and verified. The interval (2.9, 4.4) provides convincing statistical evidence for which of the following claims?

• The mean number of elk to cross a field protected by a fence is 4 per month.

• The mean number of elk to cross a field protected by a fence is 2 per month.

• The mean number of elk to cross all fields protected by a fence is greater than 2 per month.

• The mean number of elk to cross all fields protected by fence is less than 2 per month.

• The mean number of elk to cross all fields protected by fence is equal to 3.65 per month.

• More than half the students were absent because of illness.

• More than one-third of the students were absent because of oversleeping or college visits.

• the reason given the least number of times was did not finish assignment

• Only 7 students were absent because they did not finish an assignment.

• Less than one-fourth of the students were absent because they overslept.

Independent random samples of students were taken from two high schools, R and S, and the proportion of students who drive to school in each sample was recorded. The difference between the two sample proportions (R minus S) was 0.07. Under the assumption that all conditions for inference were met, a hypothesis test was conducted where the alternative hypothesis was the population proportion of students who drive to school for R was greater than that for S. The p-value of the test was 0.114. Which of the following is the correct interpretation of the p-value?

• The probability of selecting a student from high school R who drives to school is 0.07, and the probability of selecting a student from high school S who drives to school is 0.114.

• If the proportion of all students who drive to school at R is greater than the proportion who drive to school at S, the probability of observing that difference is 0.114.

• If the proportion of all students who drive to school at R is greater than the proportion who drive to school at S, the probability of observing a sample difference of at least 0.07 is 0.114.

• If the proportions of all students who drive to school are the same for both high schools, the probability of observing a sample difference of at least 0.07 is 0.114.

• If the proportions of all students who drive to school are the same for both high schools, the probability of observing a sample difference of 0.114 is 0.07.

A researcher is studying the effect of genetically modified (GM) and nongenetically modified (nGM) corn on the weight gain of lambs. The sec and genetics of the lambs can affect their weight gain. 5 sets of male twin lambs and 5 sets of female twin lambs – for a total of 20 lambs – are available for the study. The lambs will be randomly assigned to a diet of either GM or nGM diet of corn. Weight gain will be recorded for each lamb after 5 weeks on the diet. Which of the following designs would be best to use in the study?

• A completely randomized design. Randomly assign 10 lambs to the GM diet and 10 lambs to the nGM diet.

• A stratified randomized design. Divided the lambs into males and females. Within each group, randomly assign the GM diet to one half and the nGM diet to the other half.

• A randomized block design. Randomly assign 10 lambs to the GM diet and 10 lambs to the nGM diet.

• A randomized block design. Randomly assign the GM diet to the male lambs and the nGM diet to the female lambs.

• A matched pairs design. For each set of twins, randomly assign one twin to the GM diet and the other twin to the nGM diet.

• A

• B

• C

• D

• E

A sports magazine reports that the mean number of hot dogs sold by hot dog vendors at a certain sporting event is equal to 150. A random sample of 50 hot og vendors was selected, and the mean number of hot dogs sold by the vendors at the sporting event was 140. For samples of size 50, which of the following is true about the sampling distribution of the sample mean number of hot dogs sold by the vendors at the sporting event?

• For all random samples of 50 sporting events, the sample mean will be 150 hot dogs.

• For all random samples of 50 hot dog vendors, the sample mean will be 140 hot dogs.

• The mean of the sampling distribution of the sample mean is 150 hot dogs.

• The mean of the sampling distribution of the sample mean is 140 hot dogs.

• All random samples of 50 hot dog vendors will have a sample mean within 10 hot dogs of the population mean.

A business journal reports that the probability that Internet users in the United States will use a mobile payment app is 0.60. The journal claims this indicates that out of 5 randomly selected Internet users, 3 will use the mobile payment app. Is the business journal interpreting the probability correctly?

• No, because the internet users are not independent of each other.

• No, because only 60% of all people use the Internet.

• No, because 0.60 represents probability in the long run for many Internet users.

• yes, because Internet users are selected at random.

• Yes, because 3 out of 5 is equal to 60%

• The range of the distribution is 20 years.

• There were 43 people who attended the lecture.

• At least 50% of the people who attended the lecture were 43 years or younger.

• At least 75% of the people who attended the lecture were age 53 years or younger.

• At least 25% of the people who attended the lecture were 33 years old.

Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 cm. The biologists will select a random sample of crabs to measure. Which of the following is the most appropriate method to use for such an estimate?

• A one-sample z-interval for a population proportion

• A one-sample z-interval for a sample proportion

• A two-sample z-interval for a population proportion.

• A 2-sample z-interval for a difference between population proportions.

• A 2-sample z-interval for a difference between sample proportions.