. A public bus company official claims that the mean waiting time for bus number
ID: 3314822 • Letter: #
Question
. A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus 14 during peak hours on 18 different occasions. Her mean waiting time was 7.4 minutes. Assume that the standard deviation has been historically known to be 2.2 minutes. At the .05 significance level, test the claim that the mean waiting time is less than 10 minutes.
1. State the null hypothesis H0: _____________
2. State the alternative hypothesis H1: _____________
3. What is the test statistic used for the test (z or t)
4. State the significance or alpha () level
5. Determine the p-value.
6. Do you or do you not reject the null hypothesis? Why?
7. Write a clear conclusion using a complete sentence.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 10
Alternative hypothesis: < 10
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
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)
S.E = 0.519
DF = n - 1
D.F = 17
t = (x - ) / SE
t = - 5.014
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.
The observed sample mean produced a t statistic test statistic of - 5.014.
Thus the P-value in this analysis is less than 0.0001.
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
We have sufficient evidence in the favor of the claim that the mean waiting time is less than 10 minutes.
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