Can someone please help me with this statis problem? I am having trouble?

2. A researcher claims that the average cost of men’s athletic shoes is less than $60. He selects a random sample of 25 pairs of shoes with costs listed below. Is there enough evidence to support the researcher’s claim at ?





88 75 82 74 87


75 79 90 73 83


82 81 78 87 77


87 78 88 80 82


79 76 73 77 88





Small Sample Hypothesis Test)














Pre-Step: Calculate the statistics from your sample.





Mean: __________





Standard Deviation: __________





Size of Sample: __________





Step I: State the Null and Alternative Hypothesis











Step 2:





b. One-Tail or Two-Tail Test: ________________





e. Choose a Test Statistic: __________





f. Critical Value of the Test Statistic: __________





g. Label your Decision Rule:

















Step 3: Calculate the Statistic from the Data























Step 4: Clearly state your conclusion.

Can someone please help me with this statis problem? I am having trouble?
Step 1:





Mean = 80.76


Standard deviation = 5.301572094


Size of sample = 25


H0: The average cost of men's athletic shoes is not less than $60.


H1: The average cost of men's athletic shoes is less than $60.





Step 2:





One-tailed test because a direction was given


Use the t-test because population standard deviation was not given.


Critical value = -2.49 (for an alpha level of .01)


Decision rule: If t %26lt; -2.49, reject H0.





Step 3:





t = (80.76 - 60) / (5.301572094 / sqrt(25)) = 19.58





Step 4:





Do not reject the null hypothesis. There is not sufficient evidence to suggest that the average cost of men's athletic shoes is less than $60. (This result is fairly obvious given that none of the shoes in the sample were less than $60)



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