Practice Test 6 –Final Exam

Chapter 9: Hypothesis Testing Involving a Single Mean and Single Proportion

Chapter 10: Hypothesis Testing involving Two Populations: Testing Two Means and Two Proportions

Solutions

 

 

 

 

 

Problems on Chapter 9

The breaking strength of certain type of fiber used in manufacturing a certain type of cloth is required to be at least 140 psi. Past experience shows that the standard deviation of the breaking strength is 5 psi. A random sample of 40 specimens is tested and the mean breaking strength is found to be 138 psi. At a level of significance of 5%, should the fiber be judged acceptable?

1. Formulate the null and alternate hypothesis.
2. What does it mean to make a type I error in this case?
3. What does it mean to commit a type II error for this test?
4. Write the appropriate distribution and test statistics to conduct the test.

 

 

 

Suppose you want to test the following hypothesis                           

            H_o: μ ≤15

            H₁: μ > 15 

The following data is available          n = 40              x?16.5           s = 7

            α = 0.02

(a) Write the appropriate distribution and test statistics for this test (b) What is the critical value (Z-critical) and decision rule for the test?

1. 1. 3. Find the test statistics value and test the hypothesis.
      4. Use the p-value approach to test the hypothesis.

 

 

A tire manufacturer claims that the average mileage of one of its steel-belted radial truck tire is at least 50,000 miles. A sample of 100 tires revealed the sample average miles of 49,500 miles with a standard deviation of 4500 miles. Is the claim justified? Use the following methods to test your hypothesis (1) Z-value approach, (2) p-value approach, (3) critical value approach, (4) confidence interval approach. The level of significance is 5%.

 

 

A telephone company charges a flat rate for all international calls assuming that all calls last 15 minutes or less. If the calls last more than 15 minutes, a higher rate should be charged. A random sample of 35 calls show a mean call time of 17 minute with a standard deviation of 4 minutes. Should the company be charging more than the flat rate? Use a level of significance of 0.01. Use the following methods to test your hypothesis (1) Z-value approach, (2) p-value approach, (3) critical value approach, (4) confidence interval approach.

 

 

 

The mean life of certain type of batteries is 265 hours. The manufacturer of batteries claims that recent research and development work  has improved the battery life and that the battery life is significantly higher than 265 hours. A sample of 15 batteries provided the following battery life:

 

315   265   270   260   305   315   235   255   270   285  

295   245   290   255   265

 

(a) What is the sample mean life of the batteries? (b) What is the sample standard deviation?

(c) Using a=0.05, test to see if the battery life is significantly higher that 265 hours. Use (1) t-value approach, (2)critical value approach, and (3) confidence interval approach to test your hypothesis.

 

 

 

 

A recent article suggested that only 30% of the students graduating with a college degree had  job offers before they graduated. The major reason cited was a weak economy. A survey of 480 recent graduates revealed that only 128 had job offers. At the 0.05 significance level, can we conclude that the proportion of job offers differ from 30% as reported?  Use (1) Z-value approach, (2) p-value approach, (3) critical value approach, and (4) confidence interval approach to test your hypothesis. 

 

 

 

Problems on Chapter 10

 

For each of the following testing situations 1 through 4 below answer the      Questions (a) – (h):

1. Indicate if the test is two-tailed, right-tailed, or left-tailed.
2. What distribution is appropriate to conduct the test?
3. Write the test statistic.
4. Indicate the critical value or values (for example, Z _critical or t _critical). 
5. Write down the decision rule for the test.
6. What is the value of the test statistic?
7. What is your decision regarding H₀ (using Z-value or t-value approach)?
8. Find the confidence interval formula for the test and test the hypothesis using your confidence interval.   

 

 

             

Problem 8

 

Random samples from two normally distributed populations were selected with the following results:

Sample  1	Sample 2
n1 =48	n2 =60
s1 = 6.3	s2 = 7.1
x1 ? 2 5	x 2 ? 28

 

 

1. 1. Test that the mean of population 1 is less than the mean of population 2. Use a 0.10 significance level. Assume that the variances of two populations are equal.

 

1. 2. Find a 90% confidence interval for the difference between the means of the two populations. Use your confidence interval to test the hypothesis in part (a).

 

A production manager wishes to determine if there is a significant difference in the number of units produced between Monday and Friday shifts.  A random sample of these two day’s production of night shift was selected, and the number of units for each shift is recorded.  The following statistics resulted: 

 

Monday  Shift	Friday Shift
n1 =60	n2 =60
s1 = 6.4	s2 = 5.9
x1 ?27.4	x 2 ?18.3

 

1. Test the hypothesis that there is no significant difference in the number of        Production units between Monday and Friday shifts. State your hypothesis and           use the Z-value approach with a 5% level of significance.
2. Use the p-value approach to test the hypothesis in part (a).
3. Use the critical value approach to test the hypothesis in part (a).                          
4. Find a 95% confidence interval for the difference in the mean number of                        production units. Use your confidence interval to test the hypothesis in part (a).
5. Calculate a 99% confidence interval for the difference between the two means.        Compare the confidence intervals to part (d) and comment on the length of the       intervals.

 

Recently, the number of accidents in certain intersections of a city has gone up despite traffic lights. The city traffic department suggested that an advanced traffic control system that uses computer-controlled traffic lights should be implemented to reduce the accidents. The traffic department suggested installing new traffic lights on selected intersections.  Ten intersections were chosen at random, and the new traffic lights at those intersections were installed. The number of accidents during a three month period after new lights were recorded and compared to the number of accidents before new lights were installed. Using a 0.01 level of significance, test