Inference Mixture Questions

A study reports that 75 percent of young adults in a county get their news from online sources. A sociologist

believes that the percentage is actually greater than 75 percent. The sociologist will select a random sample of young adults from around the county to interview. Which of the following is the most appropriate method for investigating the sociologist’s belief?

• A one-sample z-test for a difference in population proportions

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

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

• A two-sample -z test for a difference in population proportions

• A two-sample -z test for a difference in sample proportions

A random sample of 100 people from Country S had 15 people with blue eyes. A separate random sample of 100

people from Country B had 25 people with blue eyes. Assuming all conditions are met, which of the following is a

95 percent confidence interval to estimate the difference in population proportions of people with blue eyes

(Country S minus Country B) ?

• (-0.01, 0.21)

• (-0.15,-0.05)

• (-0.19,-0.01)

• (-0.21, 0.01)

• (-0.24,0.04)

Tags

CCSS.HSS.IC.B.4

A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in Colorado. To estimate the difference between the proportions of deer with chronic wasting disease in two different

regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained

from the other region. The biologist checked for the following (see pic). Which of the following conditions for inference was the biologist checking?

• The population of deer within each region is approximately normal.

• It is reasonable to generalize from the samples to the populations.

• The samples are independent of each other.

• The observations within each sample are close to independent.

• The sampling distribution of the difference in sample proportions is approximately normal.

A random sample of 240 adults over the age of 40 found that 144 would use an online dating service. Another

random sample of 234 adults age 40 and under showed that 131 would use an online dating service. Assuming all

conditions are met, which of the following is the standard error for a 90 percent confidence interval to estimate the

difference between the population proportions of adults within each age group who would use an online dating

service?

Tags

CCSS.HSS.IC.B.4

A marketing executive is investigating whether this year’s advertising campaign has resulted in greater mean sales

compared with last year’s mean sales. The executive collects a random sample of 100 customer orders from a large

population of orders and calculates the sample mean and sample standard deviation. Which of the following is the appropriate test for the executive’s investigation?

• A one-sample z-test for a population mean

• A one-sample t-test for a population mean

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

• A two-sample t-test for a difference between means

• A matched-pairs t-test for a mean difference

A report on a certain fast food restaurant states that, the mean order total, is $9. The manager of the restaurant

believes the mean is higher. A random sample of orders will be selected. The sample mean will be calculated and

used in a hypothesis test to investigate the belief. Which of the following is the correct set of hypotheses?

White blood cell counts are normally distributed with mean 7500 and variance 500. If a patient has taken 50 laboratory blood tests that have a mean of 6899.75 and a standard deviation of 393.44, does this give evidence that his white blood cell count is significantly different than normal?

• One-Sample T Test for a Mean
• One-Sample Z Test for a Proportion
• One-Sample Z Test for a Mean
• One-Sample T Test for a Proportion

Which two factors provide evidence to state that the sampling distribution of X-bar is approximately normal?

• the population is stated as approximately normal

• n is greater than or equal to 30

• the population is stated as symmetric

A medical researcher wishes to investigate the effectiveness of exercise versus diet in losing weight.  Two groups of 25 overweight adult subjects are used, with a subject in each group matched to a similar subject in the other group on the basis of a number of physiological variables.  One of the groups is placed on a regular program of vigorous exercise but with no restriction on diet, and the other is placed on a strict diet but with no requirement to exercise.  The weight losses after 20 weeks are determined for each subject, and the difference between matched pairs of subjects (weight loss of subject in exercise group - weight loss of matched subject in diet group) is computed.  The mean of these differences in weight loss is found to be 2 lb with standard deviation sₓ = 4 lb.  Is this convincing evidence of a difference in mean weight loss for the two methods?  To answer this question, you should use

• 2 sample t test for μₓ

• one-sample z interval for μₓ
• one-proportion z interval
• paired t test for μₓ

Tags

CCSS.HSS.IC.B.4

What test would be appropriate if we wanted to show evidence for the difference in average ages at which teachers and plumbers retire?

• Matched Pairs t-test

• 2-Sample t-test