A certain pen has been designed so that true mean writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hours. A random sample of 17 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. The relevant hypotheses are H0: μ = 10 versus Ha: μ < 10. (a) If t = −2.1 and ? = 0.05 is selected, what conclusion is appropriate? -Reject -Fail to reject (b) If t = −1.73 and ? = 0.01 is selected, what conclusion is appropriate? -Reject -Fail to reject (c) If t = 0.27, what conclusion is appropriate? -Reject -Fail to reject
A certain pen has been designed so that true mean writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hours. A random sample of 17 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. The relevant hypotheses are H0: μ = 10 versus Ha: μ < 10.
(a) If t = −2.1 and ? = 0.05 is selected, what conclusion is appropriate?
-Reject
-Fail to reject
(b) If t = −1.73 and ? = 0.01 is selected, what conclusion is appropriate?
-Reject
-Fail to reject
(c) If t = 0.27, what conclusion is appropriate?
-Reject
-Fail to reject
Give as much information as you can about the P-value of a t test in each of the following situations. (Round your answers to three decimal places.)
a. upper-tailed test, n = 13, t = 3.5
b. lower-tailed test, n = 22, t = −4.1
c. upper-tailed test, df = 7,t = 2.0 = 0.043
A report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees is $62,945. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers resulted in a mean offer of $63,400 and a standard deviation of $3,900. Do the sample data provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945? Test the relevant hypotheses using ? = 0.05.
Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)
| t | = | |
| P-value | = |
State your conclusion.
a. Fail to reject H0. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945.
b. Fail to reject H0. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945.
c. Reject H0. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945.
d. Reject H0. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,945.
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