The accompanying data table lists the weights of male colleg

The accompanying data table lists the weights of male college students in kilograms. Test the claim that male college students have a mean weight that is less than the 84 kg mean weight of males in the general population. Use a 0.01 significance level. Identify the null hypothesis. alternative hypothesis. test statistic, P-value, and conclusion for the test. Assume this is a simple random sample. a) Step 1 ? STATE: Write down the question you are going to answer, and the level of significance you are going to use. Use a complete sentence which is worded in terms of this particular problem (weights of college age males). b) Step 2 ? PLAN: Identify the Null and Alternative Hypotheses. For this step, write each hypothesis in symbols AND in words, using complete sentences to say what each hypothesis means in terms of this problem. e) Step 3 ? SOLVE: Calculate the Test Statistic and find the P-value. Show your work on the calculation (INCLUDE THE STATCRUNCH SUMMARY STATS FROM YOUR MSL HOMEWORK PROBLEM), and explain how you arrived at your p- value. d) Step 4? CONCLUDE: Say whether you reject or do not reject the null hypothesis (based on the p-value from Step 3), and then write your conclusion in a complete sentence in terms of the problem. Hint: your conclusion is the answer to the question you posed in Step 1.

Solution

(a)Test the claim that male college students have a mean weight that is less than the 84kg mean weight of males in the general population

level significance=0.01

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(b) Let mu be the population mean

Null hypothesis: mu =84 (i.e. male college students have a mean weight that is equal to the 84kg mean weight of males in the general population)

Alternative hypothesis: mu<84 (i.e. male college students have a mean weight that is less than the 84kg mean weight of males in the general population)

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(c)

sample size =n=32

sample mean=72.59375

sample standard deviation =10.39807

The test statistic is

Z=(xbar-mu)/(s/vn)

=(72.59375-84)/(10.39807/sqrt(32))

=-6.21

It is a left-tailed tset.

So the p-value= P(Z<-6.21) =0 (from standard normal table)

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(d) Since the p-value is less than 0.01, we reject the null hypothesis.

So we can conclude that male college students have a mean weight that is less than the 84kg mean weight of males in the general population