(Use Excel) A police officer is concerned about speeds on a certain section of I
ID: 3257701 • Letter: #
Question
(Use Excel) A police officer is concerned about speeds on a certain section of Interstate 95. The data accompanying this exercise show the speeds of 40 cars on a Saturday afternoon. Use Table 2. a. The speed limit on this portion of Interstate 95 is 63 mph. Specify the competing hypotheses in order to determine if the average speed is greater than the speed limit. H_0: mu = 63: H_A: mu notequalto 63 H_0: mu greaterthanorequalto 63: H_A: mu 63 b. Specify the critical value(s) for the test at the 1% significance level. (Round your answer to 3 decimal places.) c. Use Excel to calculate the value of the test statistic. (Round your answer to 3 decimal places.)Explanation / Answer
Solution:-
a). Null hypothesis: < 63
Alternative hypothesis: > 63
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too large.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Critical value
z = 1 - (0.1/2)
= 1 - 0.05 = 0.95
Referring the Z table, we have the Z critical value as -2.3263
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n) = 3.3741 / sqrt(40) = 3.3741/6.324555320 = 0.53349
DF = n - 1 = 40 - 1 = 39
t = (x - ) / SE = (65 - 63)/0.53349 = 3.74889876099 or 3.7489 or 3.749
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
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