An article in the San Jose Mercury Mews stated that students

An article in the San Jose Mercury Mews stated that students in the California state university system take 4. 5 years, on average to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5. 1 with a sample standard deviation of 1. 2. Do the data support your claim at the 1% level? 80. Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life Feeling more enriched. For some reason that she can?t quite figure out, most people don?t believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think?

Solution

(77) Let mu be the population mean

The test hypothesis:

Ho: mu=4.5 (i.e. null hypothesis)

Ha: mu > 4.5 (i.e. alternative hypothesis)

The test statistic is

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

=(5.1-4.5)/(1.2/sqrt(49))

=3.5

It is a right-tailed test.

Given a=0.01, the critical value is Z(0.01) = 2.33 (from standard normal table)

The rejection region is if Z>2.33, we reject the null hypothesis.

Since Z=3.5 is larger than 2.33, we reject the null hypothesis.

So we can conclude that the data support my claim

-------------------------------------------------------------------------------------------------------------

(80) Ho: p=0.6

Ha: p not equal to 0.6

The test statisitc is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(34/64-0.6)/sqrt(0.6*0.4/64)

=-1.12

It is a two-tailed test.

Assume that the significant level a=0.05

The critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject the null hypothesis.
Since Z=-1.12 is between -1.96 and 1.96, we reject the null hypothesis.

So we can not conclude that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched