Hypothesis Test AP Stat

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: p=.21
  Ha: p > .21

• Ho: p< .21
  Ha: p= .21

• Ho: p> .21
  Ha: p= .21

• Ho: p= .21
  Ha: p< .21

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

The probability of observing a value for a test statistic at least as far from the hypothesized value as the statistic value actually observed if the null hypothesis is true is called...

• P-Hat

• One-Proportion z-test

• Z*

• P-Value

A Type I error is when: 

• We obtain the wrong test statistic

• We reject the null hypothesis when it is actually true

• We fail to reject the null hypothesis when it's actually false

• We reject the alternate hypothesis when it's actually true

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures

• Pythagorean Theorem

• t procedures

• np > 10 and n(1-p) > 10

The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes.  What is the probability that a random sample of 40 students will have a mean completion time greater than 25 minutes?

• 0.9678

• 0.0322

• 0.0344

• 0.3851

A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed 60 times.  The probability that more than 1/3 of the tosses are heads is closest to 

• 0.9951

• 0.33

• 0.109

• 0.09

A claimed psychic was presented with 200 cards face down and asked to determine if the card was one of five symbols: a star, cross, circle, square, or three wavy lines.  The "psychic" was correct in 50 cases.  To determine if he has ESP, we test the hypothesis H₀:  p = 0.20, Hₐ: p > 0.20, where p represents the true proportion of cards for which the psychic would correctly identify the symbol in the long run.  Assume the conditions for inference are met.  The P-value is 

• between .10 and .05

• between .05 and .025

• between .025 and .01

• between .01 and .001

A medical researcher wishes to investigate the effectiveness of exercise versus diet in losing weight.  Two groups of 25 overweight adult subjects are used, with a subject in each group matched to a similar subject in the other group on the basis of a number of physiological variables.  One of the groups is placed on a regular program of vigorous exercise but with no restriction on diet, and the other is placed on a strict diet but with no requirement to exercise.  The weight losses after 20 weeks are determined for each subject, and the difference between matched pairs of subjects (weight loss of subject in exercise group - weight loss of matched subject in diet group) is computed.  The mean of these differences in weight loss is found to be 2 lb with standard deviation sₓ = 4 lb.  Is this convincing evidence of a difference in mean weight loss for the two methods?  To answer this question, you should use

• one-proportion z test

• one-sample z interval for μₓ

• one-proportion z interval

• one-sample t test for μₓ

An SRS of 100 teachers showed that 64 owned smartphones.  An SRS of 100 students showed that 80 owned smartphones.  Let pₑ be the proportion of all teachers who own smartphones, and let pₓ be the proportion of all students who own smartphones.  A 95% confidence interval for the difference pₑ - pₓ is 

• (0.264, 0.056)

• (0.098, 0.222)

• (-0.222, -0.098)

• (-0.283, -0.038)