1207 mean of a sample of 48 different departure delay times for American Airline
ID: 3358944 • Letter: 1
Question
1207 mean of a sample of 48 different departure delay times for American Airline flights from New York 03 (JFK) to Los Angeles is 10.5 minutes and the standard deviation is 30.8 minutes. Use a 0.10 significance level and follow the steps for the P-Value Method below to test the claim that the mean departure delay time for all such flights is less than 12.0 minutes (4 pes) a) State the null and alternative hypotheses, and identify the claim. Ho: b) Draw a picture of the distribution and indicate the type of test. Circle the test type Left-tailed Right-tailed Two-tailed 4 pts) c) Calculate the test statistic and find the P-value for this hypothesis test. Round the Pavalue to 3 significant (4 pts) figures. You must show your work, or the calculator function you used and your input, in order to get full credit d) Use your answers to parts (b) and (c), to make a decision. (2 ptas) Circle the correct decision: Reject Ho Fail to Reject Ho e) Write your conclusion using regular words that address the original claim. (2 pts)Explanation / Answer
Solution:-
a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 12
Alternative hypothesis: < 12
b) Note that these hypotheses constitute a one-tailed test. This is left tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. 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 = 4.45
DF = n - 1 = 48 - 1
D.F = 47
c)
t = (x - ) / SE
t = - 0.34
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 - 0.34. We use the t Distribution Calculator to find P(t < - 0.34)
Thus the P-value in this analysis is 0.368.
d) Interpret results. Since the P-value (0.368) is greater than the significance level (0.01), we cannot reject the null hypothesis.
e) From the above test we do not have sufficient evidence in the favor of the claim that mean departure delay time for all such flights is less than 12.0 minutes.
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