Statistical Inference Review

• The probability the experiment correctly indicates the presence of teeth whitening attributes that do exist.

• The probability the experiment mistakenly indicates the presence of teeth whitening attributes that do not exist

• The probability the experiment correctly does not indicate the presence of teeth whitening attributes that do not exist.

• The probability the experiment mistakenly does not indicate the presence of teeth whitening attributes that do exist.

• The probability the experiment correctly indicates the need for teeth whitening.

Answer explanation

Power is the probability of correctly rejecting a false null hypothesis. In this context, that means the experiment correctly indicates the presence of teeth-whitening attributes that do exist.

A high school has six math teachers and six science teachers. When comparing their mean years of experience, which of the following is most appropriate?

• A two-sample z-test of population means

• A two-sample t-test of population means

• A one-sample z-test on a set of differences

• A one-sample t-test on a set of differences

• None of these are appropriate

Answer explanation

With such small populations, censuses rather than samples are used and there is no need for a test.

When leaving for school on an overcast morning, you make a judgement on the null hypothesis: The weather will remain dry. What would the results be of Type I and Type II errors?

• Type I Error: get drenched

  Type II Error: needlessly carry an umbrella

• Type I Error: needlessly carry an umbrella

  Type II Error: get drenched

• Type I Error: carry an umbrella and it rains

  Type II Error: carry no umbrella, but weather remains dry

• Type I Error: get drenched

  Type II Error: carry no umbrella, but weather remains dry

• Type I Error: get drenched

  Type II Error: carry an umbrella and it rains

Answer explanation

A Type I error means that the null hypothesis is correct (the weather will remain dry), but you reject it (thus you needlessly carry an umbrella).

A Type II error means that the null hypothesis is wrong (it will rain), but you fail to reject it (thus, you get drenched).

Before televised debates, a poll of 800 registered voters showed 560 in favor of a particular candidate. After the debates, a poll of 600 voters showed 450 in favor of the candidate. What is the test statistic to show if there is sufficient evidence that the candidate's popularity has increased?

Answer explanation

 Plug the values for p_C, n₁ and n₂ into the formula

Two confidence interval estimates from the same sample are (72.2, 77.8) and

(71.3, 78.7). One estimate is at the 95% level and the other is at the 99% level.

Which is which?

• (72.2, 77.8) is the 95% level

• (72.2, 77.8) is the 99% level

• The question cannot be answered without knowing the sample size

• This question cannot be answered without knowing the sample standard deviation

• This question cannot be answered without knowing both the sample size and standard deviation

Answer explanation

The narrower interval corresponds to the lower confidence level

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 that it is 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 farther 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.

Answer explanation

The null hypothesis is never accepted as true.

The alternative hypothesis is the one that uses < or > if it's one sided.

When a true parameter value is farther from the hypothesized value it becomes easier to reject the null hypothesis.

Increasing the sample size makes it easier to conclude that a difference is significant.

A confidence interval estimate is determined from the summer earnings of an SRS of n students. All other things being equal, which of the following will result in a smaller margin of error?

• A greater confidence level

• A larger sample standard deviation

• A larger sample size

• Accepting less precision

• Introducing bias into sampling

Educators investigated whether the mean number of hours that children spend watching television before they enter kindergarten has dropped from the previous estimate of 5,000. In a survey of a large sample of five-year-old children entering kindergarten, the sample mean was 4,900 hours with a P-value of 0.075. Which of the following statements is the best interpretation of the P-value?

• The probability the null hypothesis is true is 0.075

• The probability the alternative hypothesis is true is 0.075

• The probability of observing a sample mean of 4,900 is 0.075

• If the null hypothesis is true, The probability of observing a sample mean of 4,900 or less is 0.075

• If the null hypothesis is true, The probability of observing a sample mean of 4,900 or more is 0.075

Answer explanation

The P-value is the conditional probability of calculating a test statistic as extreme or more extreme if the null hypothesis is true.

A survey of a random sample of 950 U.S. Army enlistees found that 26% couldn't read training manuals written at the 7th grade level. A hypothesis test will be used to determine whether the data provide convincing evidence that over 24% of U.S. Army enlistees can't read training manuals written at the 7th grade level.

Which of the following is the test statistic for the appropriate test?

Answer explanation

The appropriate test is a one sample z-test using the formula shown.

• This cannot be answered without knowing the sample mean.

Answer explanation

If 50 is in the 99% confidence interval, it is reasonable for the mean to equal 50. Therefore, we should not reject the null hypothesis