WorksheetsAP Statistics Inference Identification
Total questions: 35
Worksheet time: 58mins
Power =1-P(Type II)
Lower Type II = Higher Alpha
Check out that formula chart...again!
Which of the following is the z critical value for a 99% confidence level?
2.33
2.58
2.97
3.09
3.29
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
I and III
III and IV
II and IV
I, II, and III
All of the above conditions must be met
What size is needed to achieve a margin of error of 3% with 95% confidence when the population proportion of successes is 0.36?
984
983
256
255
250
Which of the following would increase the width of a confidence interval?
Increasing the sample size
Decreasing the degrees of freedom
Decreasing the confidence level
Decreasing the standard deviation
Increasing the point estimate
In a sample of 64 children who received a new antibiotic for an infection, 52 of the children had positive results within 12 hours. Find a 95% confidence interval for the proportion of children with infections who will experience positive results within 12 hours when treated with the new antibiotic. Assume all conditions for inference are met.
0.81±0.096
0.81±0.080
0.81±0.071
0.81±0.079
0.81±0.094
Which of the following statements about the width of a confidence interval is true if the sample size is doubled?
The confidence interval is wider
The confidence interval is narrower
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 community wants to see if there is enough support to hold a town children's festival. 42% of 150 residents said they would participate in the event. What is the approximate standard error of p-hat?
0.03
0.24
0.02
0.04
0.002
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 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
The p-value calculated was smaller 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?
Ha is rejected and the null hypotheses is true
H0 is not rejected and the null hypothesis is false
H0 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 Type II error occurs in which of the following situations?
Ha is rejected and the null hypotheses is true
H0 is not rejected and the null hypothesis is false
H0 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 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 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 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.
z= (25-28) / 2.5 , with df=39
t= (25-28) / (2.5/√39) , with df=39
t= (25-28) / (2.5/√40) , 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.
No, z=0.49 P-value=0.312
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
The prom committee is thinking about changing the location of the prom. The new location is more expensive to rent, and for the increased cost to be reasonable, they would want to be fairly certain that more than 46% of the senior class would attend the prom. A survey of a random sample of 52 seniors found that 25 would attend if the site changed. Which of the following pairs of hypotheses should the prom committee test?
Ho: μ= 46%, Ha: μ > 46%
Ho: μ= 46%, Ha: μ≠ 48%
Ho: p= 0.46, Ha: p > 0.46
Ho: p= 0.46, Ha: p≠ 0.46
H0: p= 0.46, Ha: p < 0.46
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 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.
The alternative hypothesis states that more than 60% of the teens are exceeding the speed limit.
Which of the following is closest to the P-value associated with a two-tailed t test with 20 degrees of freedom if the value of the test statistic is 2.0?
0.001
0.01
0.03
0.05
0.10
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?
Move the equipment to three randomly chosen new locations.
Change α= 0.05 to α= 0.02.
Carry out a two-sided test instead of a one-sided test.
Increase the sample size to 60 pieces of equipment being tested.
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 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.
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.
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?
Yes. Since the interval contains zero there is strong evidence that the mean number of traffic violations is greater for males than females.
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 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.
In a random sample of 300 elderly men, 65% were married, while in a random sample of 400 elderly women, 48% were married. Which of the following is the 99% confidence interval estimate for the difference between the proportion of the elderly women who are married? Assume all conditions for inference are met.
0.17 ± 0.073
0.17 ± 0.096
0.55 ± 0.067
0.56 ± 0.067
0.565 ± 0.096
Which of the following statements are not true?
1) When samples are paired, a two-sample t test is appropriate.
2) The degrees of freedom for a paired t test is n-1, where n is the sum of the two sample sizes.
3) A two-sample z-test is used to test hypotheses about p1-p2 with large independent samples
1 only
2 only
3 only
1 and 2
1 and 3
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?
One-sample z test for a population mean
One-sample z test for a population proportion
Two-sample t test for population means
Paired 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)
We don't know that they are random samples from both companies
The samples may not be independent
The sample size is not large enough
A school district wishes to estimate the difference in the proportion of girls who purchase a school lunch and the proportion of boys who purchase a school lunch. Assuming that the conditions for inference are met, which of the following confidence intervals would be appropriate?
A one-sample t interval
A two-sample t interval
A paired t interval
A one proportion z interval
A two proportion z interval
