Which of the following is a difference between a t interval and a z interval?

z intervals are used if you know the population standard deviation and t intervals are used when you do not know the population standard deviation

t intervals are used if you know the population standard deviation and z intervals are used when you do not know the population standard deviation

t intervals are used when the sample size is large and z intervals are used when the sample size is small

z intervals are used when the population is not normally distributed

t intervals can only be used when the sample size is large whereas z intervals can be used for both large and small samples

Assuming that the data came from a random sample from the population of interest, what other conditions must be met in order for the z interval to be an appropriate way to estimate a population proportion? I. n≥30 or the population distribution is approximately normal II. The population size is at least ten times greater than the sample size III. The population standard deviation is known IV. nṗ≥10 and n(1-ṗ)≥10

All of the above conditions must be met

Which of the following would increase the width of a confidence interval?

Decreasing the degrees of freedom

Decreasing the confidence level

Decreasing the standard deviation

Which of the following statements about the width of a confidence interval is true if the sample size is doubled?

The confidence interval is narrower

The confidence interval is wider

It will have no effect on the width of the confidence interval

The width of the confidence interval will double

The width of the confidence interval will be half as wide

A psychologist reports that the result of a hypothesis test was statistically significant at the 0.05 level. Which of the following is consistent with this statement?

The p-value calculated was smaller than the significance level of 0.05

The significance level calculated was larger than 0.05

The significance level calculated was smaller than 0.05

The p-value calculated was larger than the significance level of 0.05

There was not enough information to make a decision

A Type I error occurs in which of the following situations?

H 0 is rejected and the null hypothesis is true

H a is rejected and the null hypotheses is true

H 0 is not rejected and the null hypothesis is false

The p-value is too small to reject the null hypothesis

The α level is too large and so the null hypothesis is rejected

A Type II error occurs in which of the following situations?

H 0 is not rejected and the null hypothesis is false

H a is rejected and the null hypotheses is true

H 0 is rejected and the null hypothesis is true

The p-value is too small to reject the null hypothesis

The α level is too large and so the null hypothesis is rejected

A graduate student at a private university wanted to study the amount of money that students at his university carried with them. A recent study reported that the average amount of money carried by college students is $31. He decides to collect data and carry out a test to see if there is evidence that the average is higher for students at his university. Which of the following describes a Type II error in this context?

This would lead to the incorrect idea that there was no reason to believe that students at his university carry, on average, more than $31

This would lead to the incorrect idea that students at his university, on average, spend more money each month than students at other universities

This would lead to the incorrect idea that students at his university carry, on average, more than $31

This would lead to the incorrect idea that students at his university carry, on average, less than $31

This would lead to the correct idea that students at other campuses carry, on average, less than $31

Neutering dogs is common surgical practice. The mean time to recover from the general anesthetic used is 28 hours. veterinarian believes that since changing to a new anesthetic, the mean recovery time is shorter than before. To investigate, she selects a random sample of 40 surgeries done with the new anesthetic and finds that the mean recovery time was 25 hours and the standard deviation was 2.5. She plans to use this sample data to test to see if there is evidence that the recovery time is shorter. Which of the following is the correct test statistic for this study? Assume conditions for inference have been met.

t= (25-28) / (2.5/√40) , with df=39

t= (25-28) / (2.5/√39) , with df=39

t= (25-28) / (2.5/√40) , with df=40

t= (25-28) / (2.5/√39) , with df=40

Bicycles purchased from a discount store come unassembled. The assembly instructions that come with the bicycle claim that the average assembly time is 30 minutes. A consumer group has received complaints from people who say that the assembly tie was greater than the time claims. They decide to purchase 40 of these bikes and have asked 40 different people to assemble them. The consumer group believed that it was reasonable to regard these 40 people as representative of the population of people who might purchase this bike. For this sample, they found that the assembly imes had a mean of 34.2 minutes and a standard deviation of 8.6 minutes. Is there convincing evidence that the claimed average assembly time is too low? Test at the 0.05 significance level. Assume conditions for inference have been met.

Yes, t=3.09, df=39, P-value=0.002

Yes, t=3.05, df=39, P-value=0.004

No, t=0.49, df=39, P-value=0.313

Yes, t=3.05, df=40, P-value=0.002

A local group claims that more than 60% of the teens driving after 10 p.m. are exceeding the speed limit. They plan to collect data in hopes that a hypothesis test will provide convincing evidence in support of their claim. Which of the following is true about the hypotheses the group should test?

The alternative hypothesis states that more than 60% of the teens are exceeding the speed limit.

The null hypothesis states that less than 60% of the teens are exceeding the speed limit.

The null hypothesis states that more than 60% of the teens are exceeding the speed limit.

The alternative hypothesis states that less than 60% of the teens are exceeding the speed limit.

The alternative hypothesis states that less than or equal to 60% of the teens are exceeding the speed limit.

A study by a geological research team found that a new piece of equipment designed to measure the forces of an earthquake is not effective. They based this conclusion on data from a sample of 40 pieces of equipment and they carried out a test with α= 0.05. The manufacturer of the equipment claims this study was flawed and that their equipment is good. The research team is considering carrying out a second study with the intention of increasing the power of the test. Which of the following would ensure an increase in the power of the test?

Increase the sample size to 60 pieces of equipment being tested.

Move the equipment to three randomly chosen new locations.

Carry out a two-sided test instead of a one-sided test.

Decrease the sample size to 20 pieces of equipment being tested.

Suppose the mean height of a woman in the United States is 64.5 in. with a standard deviation of 2.5 in. A clothing designer feels that women who use her products may actually be taller on average. She selects a random sample of 70 women from all women who have previously purchased her clothing. What is the population of interest, and what test would the designer use to test her claim?

The population is all women who have previously purchased the designer's clothing and the appropriate test is a z test with σ=2.5.

The population is all women in the United States and the appropriate test is a t test with df= 70.

The population is all women in the United States and the appropriate test is a z test with σ= 2.5.

The population is all women who have previously purchased the designer's clothing and the appropriate test is a t test with df= 70.

The population is all women who have previously purchased the designer's clothing and the appropriate test is a t test with df= 69.

Insurance companies charge higher monthly premiums for male drivers than female drivers between the ages of 16 and 25. Their rationale is that male drivers have more traffic violations that females. A consumer group believes this rationale is no longer appropriate. To investigate, a random sample of male drivers and a random sample of female drivers in the target age groups were selected. Each person was asked how many traffic violations they have received. The resulting data was used to compute the given summary statistics. A 98% confidence interval for the difference in population mean number of traffic violations is (-1.3, 1.5). Based on this confidence interval, is there evidence that the population means are different?

No. Since the interval contains zero, it is plausible that the mean number of traffic violations is greater for males than females.

Yes. Since the interval contains zero there is strong evidence that the mean number of traffic violations is greater for males than females.

Yes. Since the interval does not contain zero, there is strong evidence that the mean number of traffic violations is greater for males than females.

No. Since the interval does not contain zero, there is insufficient evidence that the number of traffic violations is the same for males and females.

Yes. Since the interval is wider for positive numbers, there is evidence that the mean number of traffic violations is greater for males than females.

A new classroom strategy uses interactive technology to review information for a test. A random sample of 40 classroom teachers has been asked to use the technology with one of their classes and not with another class. The average test score for each class is then recorded for each teacher. Which would be the appropriate test to run to see if the technology helped?

Paired t test for population means

One-sample z test for a population mean

One-sample z test for a population proportion

Two-sample t test for population means

Two-sample z test for population means

A soup manufacturer is deciding which company to use for their mushroom purchases. A random sample of 20 mushrooms for each company found 30% of the mushrooms from one company were damaged and 35% from the other company were damaged. What assumptions for the two proportions z test would be a concern? (select all that apply)

The sample size is not large enough

We don't know that they are random samples from both companies

The samples may not be independent

AP Statistics Inference Review

Authored by Barbara White

Mathematics

11th Grade - University

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Hint: remember that lovely formula chart

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Hint
Power =1-P(Type II)
Lower Type II = Higher Alpha

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