Inference Practice

In a random sample of 1,250 adult drivers, 450 said that they would cut their driving by 10% if this significantly helped the environment. Find a 95% confidence interval estimate of the proportion of adult drivers who are will to cut their driving by 10% to help the enviornment.

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CCSS.HSS.IC.B.4

A guidance counselor is interested in comparing GPAs of students with home access to internet with students who do not have this access. She pulls the files of an SRS of 10 students who do have home access to the Internet and an SRS of 10 who do not, and proceeds to run a t-test to compare the mean GPAs of each group. Which of the following is a necessary assumption?

• The population standard deviations from each group are known.

• The population standard deviations from each group are unknown.

• The population standard deviations from each group are equal.

• The population of GPA scores for each group is normally distributed.

• The samples must by independent samples, and for each sample np and n(1-p) must but at least 10.

In general, how does doubling the sample size change the confidence interval size?

• Doubles the interval size.

• Halves the interval size.

• Multiplies the interval size by 1.414

• Divides the interval size by 1.414

• This questions cannot be answered without knowing the sample size.

Tags

CCSS.HSS.IC.B.4

A fitness center advertises that the average pulse rate of its members is 68.4 bpm. Gym members suspect this is a made-up number and run a hypothesis test on an SRS of 48 members, calculating a mean of 71.0 bpm with a standard deviation of 10.3 bpm. In which of the following intervals is the P-value located?

• P < .01

• .01 < P < .02

• .02 < P < .05

• .05 < P < .10

• p > .10

In a one-sided hypothesis test for the mean, for a random sample of size 15 the t-score of the sample mean is 2.615. Is this significant at the 5% level? At the 1% level?

• Significant at the 1% level but not at the 5% level

• Significant at the 5% level but not at the 1% level

• Significant at both the 1% level and 5% level

• Significant at neither the 1% level and 5% level

• Cannot be determined from the given information

Tags

CCSS.HSS.ID.A.4

Which of the following is a true statement?

• Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

• A well-planned test of significance should result in a statement either that the null hypothesis is true or false.

• The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.

• When a true parameter value is further from the hypothesized value, it becomes easier to reject the alternative hypothesis.

• Increasing the sample size makes it more difficult to conclude that an observed difference between observed and hypothesized values is significant.

To test whether husbands or wives have greater manual agility, an SRS of 50 married couples is chosen, and all 100 people are given a 1-minute period to find and place strangely shaped pegs into matching holes. What is the conclusion at a 5% significance level if a two-sample hypothesis test, Ho: mu1 - mu2 = 0, Ha: mu1 - m2 not = 0, results in a P-value of .15

• The observed difference between husbands and wives is significant.

• The observed difference is not significant.

• A conclusion is not possible without knowing the mean number of pegs placed by husbands and wives.

• A conclusion is not possible without knowing both the mean and SD of the number of pegs placed by husbands and wives.

• A two-sample hypothesis test should not be used in this example.

Which of the following statements is true?

• Is is helpful to examine your data before deciding whether to use a one-sided or a two-sided hypothesis test.

• If the P-value is .05, the probability that the null hypothesis is correct is .05

• The larger the P-value, the more evidence there is against the null hypothesis.

• If the P-value is small enough, we can conclude that the alternative hypothesis is true.

• We do not use sample statistics in stating hypotheses.

A quality inspector plans to test a sample of 40 bottles of soft drink labeled as 20 oz. If she finds the mean content to be less than 19.8 oz, she will have the bottling machinery stopped and recalibrated. If it is known that the machine operates with a SD of .75 oz, what is the probability that the inspector will mistakenly stop a machine that is delivering a mean of at least 20 oz per bottle?

• .023

• .046

• .050

• .092

• .119

Tags

CCSS.HSS.ID.A.4

Which of the following is a true statement?

• The P-value of a test is the probability of obtaining a result as extreme as or more extreme than the one obtained, assuming the null hypothesis is true.

• If the P-value for a test is .043, the probability that the null hypothesis is true is .043.

• When the null hypothesis is rejected, it is because it is not true.

• The greater the P-value, the greater the evidence against the null hypothesis

• A very large P-value provides convincing evidence that the null hypothesis is true.