Confidence Intervals and Hypothesis Testing

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she test?

• Ho : p<0.80

  Ha : p>0.80

• Ho : p=0.80

  Ha : p>0.80

• Ho : p>0.80

  Ha : p=0.80

• Ho : p<0.80

  Ha : p=0.80

• Ho : p=0.80

  Ha : p<0.80

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (Ho : p = 0.97 and Ha : p > 0.97). The test results in a P-value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing?

• They correctly fail to reject Ho.

• They correctly reject Ho.

• They reject Ho, making a Type I error.

• They fail to reject Ho, making a Type I error.

• They fail to reject Ho, making a Type II error.

Which of the following values below represents the critical value for a 98% confidence interval?

• 2.326

• 2.054

• 1.645

• 3.091

Identify the correct null hypothesis: Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

• H₀: p = 0.50

• H₀: µ = 100

• H₀: p = 0.48

• H₀: µ = 96

When performing a test about the population proportion, what distribution would you need to use? 

• z

• t

• chi-square

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: p > .21

  Ha: p < .21

Suppose the P-value for a hypothesis test is 0.0304. Using a = 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

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.

• True

• False

A research company wants to estimate the proportion of people who like oatmeal.  They want the confidence level to be 95%.  The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey.  What happens to the confidence interval?

• It gets larger

• It gets smaller

• It stays the same

• Too little information given