Chapter 11.6, Problem 8CYU

To determine

Identify the hypothesis and claim.

Answer to Problem 8CYU

Company’s claim that each golf tee they produce is $5$ centimetres in length can be rejected.

Explanation of Solution

Given information:

A company claims that each golf tee they produce is $5$ centimetres in length. Using a sample of $168$ tees, Angelene calculated a mean of $5.1$ centimetres with a standard deviation of $0.3$ . Test the hypothesis at $10\%$ significance.

Calculation:

Consider null hypothsis $H_0$ and alternative hypothesis is $H_a$ . It is given as,

  $\begin{array}{l}{H}_0:\mu =5\\ H_a:\mu \ne 5\end{array}$

The claim is $H_0:\mu =5$ it is null hypothesis and it is equality. $H_a:\mu \ne 5$ alternative hypothesis is competent of $H_0:\mu =5$ .

The hypothesis test for alternative $\mu \ne 5$ is a left trailed test. Now test at $10\%$ of the distribution.

Use $TI83$ calculator for value calculation,

Press $key{2}^{nd}$ and then DISTR. Choose $3^{rd}$ option.

  

Now calculate $Z-statistic$ for sample data,

  $z=\frac{\overline{x}-\mu }{\left(\frac{s}{\sqrt{n}}\right)}\mathrm{.....}\left(1\right)$

Now put the values, mean is $5.1$ cm, standard deviation of $0.3$ minutes, sample of $168$ tees equation $\left(1\right)$ .

  $\begin{array}{l}z=\frac{5.1-5}{\left(\frac{0.3}{\sqrt{168}}\right)}\\ =4.3204\end{array}$

Null hypothesis gets rejected because the $Z-statistic$ for the sample is within the critical region.

Hence, company’s claim that each golf tee they produce is $5$ centimetres in length can be rejected.