77. An article in the San Jose Mercury News stated that students in the Californ

Question

77. An article in the San Jose Mercury News 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? Solve using the following steps, similar to Appendix-E (Hypothesios Testing with One Sample Mean): b. Find the random variable X c. State the distribution you will use and why ? e. What is the P-value (probability) ? f. Will you reject or not reject the Null Hypothesis and why ?

Explanation / Answer

Set Up Hypothesis
Null, H0: U=4.5
Alternate,believe that the mean time is longer H1: U > 4.5
Test Statistic
Population Mean(U)=4.5
Sample X(Mean)=5.1
Standard Deviation(S.D)=1.2
Number (n)=49
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =5.1-4.5/(1.2/Sqrt(49))
to =3.5
| to | =3.5
Critical Value
The Value of |t | with n-1 = 48 d.f is 2.407
We got |to| =3.5 & | t | =2.407
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 3.5 ) = 0.00051
Hence Value of P0.01 > 0.00051,Here we Reject Ho

We have evidence that mean time is longer

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