STAT 200 Week 7 Solution

Week 7: Complete the following exercises showing your work. 

1) The football coach randomly selected ten players and timed how long each player took to perform a certain
drill. The times (in minutes) were:
11 8 8 10 11
9 9 14 8 5
Find a 95% confidence interval for the population standard deviation 􀎗.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim.

2) A supplier of digital memory cards claims that no more than 1% of the cards are defective. In a random sample
of 600 memory cards, it is found that 3% are defective, but the supplier claims that this is only a sample
fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective.
Solve the problem.

3) A manufacturer finds that in a random sample of 100 of its CD players, 96% have no defects. The manufacturer
wishes to make a claim about the percentage of nondefective CD players and is prepared to exaggerate. What is
the highest rate of nondefective CD players that the manufacturer could claim under the following condition?
His claim would not be rejected at the 0.05 significance level if this sample data were used. Assume that a
left-tailed hypothesis test would be performed.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim.

4) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean
weight of 183.9 lb. Assuming that 􀎗 is known to be 121.2 lb, use a 0.10 significance level to test the claim that the
population mean of all such employees weights is less than 200 lb.
Test the given claim. Use the P-value method or the traditional method as indicated. Identify the null hypothesis,
alternative hypothesis, test statistic, critical value(s) or P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim.

5) A simple random sample of 15-year old boys from one city is obtained and their
weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights
come from a population with a mean equal to 149 lb. Assume that the standard deviation of the weights of all
15-year old boys in the city is known to be 16.2 lb. Use the traditional method of testing hypotheses.
147 138 162 151 134 189 157 144 175 127 164

Assume that a simple random sample has been selected from a normally distributed population and test the given claim.
Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test
statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the
original claim.

6) A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces) of
the cereal in a random sample of 8 of its cereal packets are listed below.
14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2
Test the claim at the 0.01 significance level.
Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic,
P-value, critical value(s), and state the final conclusion.

7) Test the claim that the mean lifetime of car engines of a particular type is greater
than 220,000 miles. Sample data are summarized as n = 23, x = 226,450 miles, and s = 11,500 miles. Use a
significance level of 􀎅 = 0.01.
2
Find the critical value or values of 􀎛2 based on the given information.

8) H1: 􀎗 < 0.14
n = 23
􀎅 = 0.10
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.

9) 􀎅 = 0.08; H1 is μ 􀁊 3.24
Solve the problem.

10) A simple random sample of students is selected, and the students are asked how much time they spent
preparing for a test. The times (in hours) are as follows:
1.3 7.2 4.2 12.5 6.6 2.5 5.5
Based on these results, a confidence interval for the population mean is found to be μ = 5.7 ± 4.4. Find the degree
of confidence.
3