1. A large school district in Tennessee wants to estimate the average SAT score

ID: 3224320 • Letter: 1

Question

1. A large school district in Tennessee wants to estimate the average SAT score of this year’s graduating class. The district takes a simple random sample of 100 seniors. The sample mean is 520 and the population standard deviation for SAT scores is known to be 70. What is the 95% confidence interval for ?
A. 520 ± 2 (70)
B. 520 ± (70 / 10)
C. 520 ± 2 (70 / 10)
D. 520 ± 2 (70) (10)

2. The manufacturer of a coin claims that the mean lead content in this coin is 120 ppm. A random sample of 30 such coins is taken to evaluate the manufacturer’s claim. What is the null hypothesis?
A. H0: x   120 ppm
B. H0:   120 ppm
C. H0: x   = 120 ppm
D. H0:   = 120 ppm

3. A consumer evaluates the claim that a new candy package contains “20 percent of strawberry candies in every bag.” She recognizes that the amount of candies will vary slightly from bag to bag but suspects that the mean amount of candies per bag is actually less than 20 percent.    The advocate purchases a random sample of 40 bags of candy and calculates x to be 16.2 percent. What alternative hypothesis does she want to test?
A. Ha:   20
B. Ha:   < 20
C. Ha: x   16.2
D. Ha: x   < 16.2

4. Suppose the P-value for a hypothesis test is 0.025. Using = 0.05, what is the appropriate conclusion?
A. Reject the null hypothesis.
B. Do not reject the null hypothesis.
C. Reject the alternative hypothesis.
D. Do not reject the alternative hypothesis.

5. Psychologists recorded the size of the tip of 30 patrons in a restaurant when a message indicating that the next day’s weather would be good was written on their bill. We know that the population standard deviation is = 2.4. We want to estimate the mean percentage tip for patrons of this restaurant who receive this message on their bill within ±0.5 with 90% confidence. How many patrons must we observe? (For 90% confidence, Table C gives z = 1.645.)
A. 8
B. 53
C. 63
D. 52.4

Explanation / Answer

Answer:

mean±z*sd/sqrt(n)

4. Suppose the P-value for a hypothesis test is 0.025. Using a = 0.05, what is the appropriate conclusion?
Answer: A. Reject the null hypothesis.
B. Do not reject the null hypothesis.
C. Reject the alternative hypothesis.
D. Do not reject the alternative hypothesis.

Sample size = (z2*s2)/d2

Sample size - mean

0.5

E, error tolerance

2.4

standard deviation

90%

confidence level

1.645

62.336

sample size

rounded up