Question

A recent article in Newsweek claims that the average weight of women entering college as freshman is 135lbs. The staff at your paper thinks this estimate is high. At a significance of 0.05, test the claim that the mean weight is actually lower than 135lbs. What is the null and alternate hypothesis? What is the Critical Value, t?? What is the Test Statistic, T? Conclusion?
Then calculate the P-value. Does p-value agree support your conclusion? Why?

149.9
141.1
123.5
154.3
127.9
110.2
123.5
154.3
134.5
116.8
125.7
127.9
108.0
152.1
114.6
138.9
123.5
119.0
125.7
138.9
119.0
123.5
138.9
112.4
130.1
143.3
116.8
136.7
121.3
125.7
141.1
132.3
114.6
121.3
92.6

Answer 1

Here claim is that mean weight is less than 135 lbs

As we know null hypothesis always have equality sign, so

vs

For the given data n=35, and (using excel)

The t-critical value for a left-tailed test, for a significance level of ?=0.05 is

tc?=?1.691

Graphically

Test statistics is   

As t statistics is in rejection region we reject the null hypothesis

The P-Value is 0.002836, hence we reject the null hypothesis

So P value also support the conclusion