A sample of 42 observations is selected from one population with a population standard deviation of 3.1. The sample mean is 101.0. A sample of 52 observations is selected from a second population with a population standard deviation of 4.0. The sample mean is 99.8. Conduct the following test of hypothesis using the 0.04 significance level.
H0 : ?1 = ?2 H1 : ?1 ? ?2
(b) State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places.)
The decision rule is to reject H0 if z is outside the interval (, ).
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(e) What is the p-value? (Round your answer to 4 decimal places.)
p-value
| A sample of 42 observations is selected from one population with a population standard deviation of 3.1. The sample mean is 101.0. A sample of 52 observations is selected from a second population with a population standard deviation of 4.0. The sample mean is 99.8. Conduct the following test of hypothesis using the 0.04 significance level. |
| H0 : ?1 = ?2 |
| H1 : ?1 ? ?2 |
| (b) | State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places.) |
| The decision rule is to reject H0 if z is outside the interval (, ). |
| (c) | Compute the value of the test statistic. (Round your answer to 2 decimal places.) |
| Value of the test statistic |
| (e) | What is the p-value? (Round your answer to 4 decimal places.) |
| p-value |
Related textbook solutions
Related questions
The manufacturing specification for a particular variety of copper wire indicates that the process standard deviation of the wire diameter should not exceed .005 inches. A random sample of 20 wires reveals a sample standard deviation of .006 inches. The researcher is interested in finding evidence at the .05 level that the process standard deviation is exceeding the specification limit.
Which of the following pairs of hypotheses accurately reflects the question of interest?
| a. | H0: ?=.005 HA: ??.005 | |||||||||||||||||||||||||||||||||||||||||||||||||
| b. | H0: p?0.005 HA: p<0.005 | |||||||||||||||||||||||||||||||||||||||||||||||||
| c. | H0: ??.005 HA: ? >.005 | |||||||||||||||||||||||||||||||||||||||||||||||||
| d. | H0: ??.005 HA: ?>.005 | |||||||||||||||||||||||||||||||||||||||||||||||||
| e. | H0: ?=.005 HA: ??.005 Which of the following is the correct value of the test statistic?
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