AP Statistics Tests of Significance

Le the random variable X represent the amount of money Carl makes tutoring statistics students in the summer.  Assume that X is Normal with mean $240 and standard deviation $60.  The probability is approximately 0.6 that, in a randomly selected summer, Carl will make less than about

• $144

• $216

• $255

• $30

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

The incomes in a certain large population of college teachers have a normal distribution with mean $60,000 and standard deviation $5000.  Four teachers are selected at random from this population to serve on a salary review committee.  What is the probability that their average salary exceeds $65,000?

• 0.0228

• 0.1587

• 0.8413

• 0.9772

I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population.  Which of the following would produce a wider confidence interval, based on these same data?

• Use a larger confidence level

• Use a smaller confidence level

• Use the same confidence level, but compute the interval n times.  Approximately 5% of these intervals will be larger

• Increase the sample size

You are told that the proportion of those who answered "yes" to a poll about internet use is 0.70, and that the standard error is 0.0459.  The sample size is

• 50

• 99

• 100

• 200

The standardized test scores of 16 students have mean x̄ = 200 and standard deviation s = 20.  What is the standard error of x̄?

• 20

• 10

• 5

• 1.25

After a college's football team once again lost a football game to the college's arch rival, the alumni association decided to conduct a survey to see if alumni were in favor of firing the coach.  Let p represent the proportion of all living alumni who favor firing the coach.  Which of the following is the smallest sample size needed to guarantee an estimate that's within 0.05 of p at a 95% confidence level?

• 269

• 385

• 538

• 768

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