Chapter 9.3, Problem 2.1CYU

To determine

To check: Whether there issufficient evidence to support the suspicion of professor at 5% significance level.

Answer to Problem 2.1CYU

Yes, there is sufficient evidence to support the suspicion of professor.

Explanation of Solution

Given:

The data set is:

9	5
6	6
8	11
6	6
8	3
8	6
6	6
6	10
6.5	7
7	8
9	4.5
4	9
3	7
4	7

Formula used:

The test statistic is computed as:

  $t=\frac{\overline{x}-\mu }{\frac{s}{\sqrt{n}}}$

Here,

  $\begin{array}{l}\overline{x}=\text{Sample mean}\\ \mu \text{= Population mean}\\ n=\text{}\text{Sample size}\\ s=\text{ Sample standard deviation }\end{array}$

Calculation:

Here, $\mu$ be the average sleeping hours.

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =8\\ H_a:\mu <8\end{array}$

The obtained excel output is:

Here, p-value is 0.0006. Here, p-value

Conclusion:

Thus, at 5% significance level there is sufficient evidence to support the suspicion of professor.