Proportions Hypothesis Testing

This is the same write-up as found in the previous question:

A recent newspaper article claimed that the President’s approval rating is 46%; however, a sample of 80 U.S. citizens shows that 43 of them approve of the President’s performance. At a 0.10 level of significance, you are interested in determining if there is evidence that the President’s approval rating is actually higher.

What is the test statistic for this hypothesis test?

• t = -1.39

• z = 1.39

• t = -.538

• z = -.538

This is the same write-up as found in the previous question:

A recent newspaper article claimed that the President’s approval rating is 46%; however, a sample of 80 U.S. citizens shows that 43 of them approve of the President’s performance. At a 0.10 level of significance, you are interested in determining if there is evidence that the President’s approval rating is actually higher.

What is the p-value for this hypothesis test?

• .082

• .164

• .702

• .298

A state university wants to increase its retention rate of 4% for graduating students from previous years. After implementing several new programs, the university re-evaluated its retention rate. Identify the Type I error if Ho: p = .04 and Ha: p > .04.

• The university thinks retention is the same and stops all new programs, but in fact retention is on the rise.

• The university concludes that retention has stayed the same, but it is actually lower.

• The university concludes that retention is on the rise, but in fact the new programs do not help retention.

• The sample size was not large enough to make a valid conclusion.

The U.S. Department of Labor released the current unemployment rate for the month, claiming that

unemployment does not significantly differ from the 8.3% it was last month. However, a Gallop poll reveals

that there is a reduction in the unemployment rate. Identify the Type II error if Ho: p = .083 and Ha: p ≠ .083 .

• The conclusion is made that unemployment has changed when actually it has remained the same.

• The conclusion is made that unemployment has increased when it has actually decreased.

• The conclusion is made that unemployment is declining and the good news is released.

• The conclusion is made that there is no change in unemployment; but the rate has actually changed.

If a hypothesis test leads to a decision to fail to reject the null hypothesis,

• a Type I error may have been made

• a Type II error may have been made

• a Type I error was definitely made

• a Type II error was definitely made

The percentage of female physicians is 27%. In a survey of physicians, 45 of the 120 were women. Is there sufficient evidence at the α = 0.01 to claim that the proportion of women physicians is greater than 27%? Which is closest to the p-value?

• 0.0005

• 0.005

• 0.05

• 0.5

5% of trucks of a certain model have needed new engines after being driven between 0 and 100 miles.  The manufacturer hopes that the redesign of one of the engine's components has solved this problem.  Write the null and alternative hypotheses for this situation.

• Ho:  p < 0.05
  Ha:  p >= 0.05

• Ho:  p <= 0.05
  Ha:  p > 0.05

• Ho:  p >= 0.05
  Ha:  p < 0.05

• Ho:  p > 0.05
  Ha:  p = 0.05

A manufacturer has a set limit that the proportion of defective items is not to be over 18%. The buyer thinks the proportions of defective items exceeds the limit. The buyer take a random sample of 90 items and finds that 19 of them are defective.   The p-value is:

• 0.2333

• 0.2212

• .7788

• .7682

A study found that 68% of the population owns a home. In a random sample of 150 households, 92 owned a home. At the α = 0.01 level, is there enough evidence to reject the claim?

Which value is closest to the p-value?

• 0.02

• 0.04

• 0.06

• 0.08

Suppose the P-value for a hypothesis test is 0.0304. Using α = 0.05, what is the appropriate conclusion?

• Reject the null hypothesis

• Reject the alternative hypothesis

• Fail to reject the null hypothesis

• Fail to reject the alternative hypothesis