Question

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?

Short answer

The claim is supported at the $1\%$ level .

Step-by-step solution

Given Information

For $H_0$, mean is $=4.5$

For $H_a$, mean is$\ne 4.5$

localid="1650205190437" $\alpha =0.01$

Test$t=0.995$

$D_f=49$

Explanation

Using the formula below:

$t=\frac{(\overline{X}-\mu )}{{\displaystyle \frac{s}{\sqrt{n}}}}$

Critical Value = $2.6822$

Reject $H_0$ for$|t|>2.6822$

$t=\frac{\left(4.5-5.1\right)}{{\displaystyle \frac{1.2}{\sqrt{49}}}}=\frac{-4.2}{1.2}=-3.5$

Reject $H_0$ , p - value $=0.001$