## statistics exam

statistics exam

9 questions on topics in Ch. 7, Sections 2 – 5 and Ch. 8, Section 1

3 short response (3 points each)

6 hypothesis tests to perform (13 points each) – you will need to indicate all the steps for each test, and use both the critical-value and P-value methods.

QUESTION 1

1. Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the

critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion. Use English if you cannot write the

mathematical symbols.

A simple random sample of 10 people from a certain population has a mean age of 27. Can we conclude that the mean age of the population is not 30? The variance is

known to be 20. Let α = .05.

13 points

QUESTION 2

1. Perform the following hypothesis test using the P-value method. Be sure to state the null and alternative hypotheses, calculate the test statistic, find the

P-value, compare the P-value to the level of significance, and state the conclusion. Use English if you cannot write the mathematical symbols.

Suppose a high school principal claims that the mean SAT score in math at his school is better than 550. A random sample of 72 students has a mean score of 574. Assume

that the population standard deviation is 100. Is the principal’s claim valid at the .10 level?

13 points

QUESTION 3

1. If Problem #2 was a two-tailed test, what would the P-value be?

3 points

QUESTION 4

1. Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the

critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion. Use English if you cannot write the

mathematical symbols.

Suppose the mean weight of King Penguins found in an Antarctic colony last year was 15.4 kg. In a sample of 35 penguins this year from the same colony, the mean

penguin weight is 14.6 kg with a standard deviation of 2.5 kg. At the .05 significance level, can we reject the null hypothesis that the mean penguin weight does not

differ from last year?

15 points

QUESTION 5

1. Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the

critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion. Use English if you cannot write the

mathematical symbols.

An airline claims that, on average, 5% of its flights are delayed each day. On a given day of 500 flights, 6.2% were delayed. Test the hypothesis that the average

proportion of delayed flights is greater than 5%. Use α = 0.01.

15 points

QUESTION 6

1. If the sample proportion in Problem #6 was 37 of 500, what would the test statistic equal?

3 points

QUESTION 7

1. Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the

critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion. Use English if you cannot write the

mathematical symbols.

The television habits of 30 children were observed. The sample mean was found to be 48.2 hours per week, with a standard deviation of 12.4 hours per week. Test the

claim that the standard deviation for all children is no more than 16 hours per week. Use 10% confidence.

13 points

QUESTION 8

1. If the test in Problem #8 was two-tailed and used 5% confidence, what would the critical values be?

3 points

QUESTION 9

1. Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the

critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion. Use English if you cannot write the

mathematical symbols.

The mean lasting time of 2 competing floor waxes is to be compared. Twenty floors are randomly assigned to test each wax. Wax#1 had a mean time of 3 months, while

Wax#2’s mean was 2.9 months. The population standard deviations are 0.33 and 0.36, respectively. Does the data indicate that Wax#1 lasts longer than Wax#2? Test at a

5% level of significance.