Chapter 12.6, Problem 27PPS

To determine

To Conduct :A hypothesis test with the help of given information.

Explanation of Solution

Given information:

Lamar tested 40 random cookies.

Use the data below to conduct a hypothesis test:

21	19	20	20	19	19	18	21	19	17
19	18	18	20	20	19	18	20	18	19
21	21	19	17	17	18	19	19	19	21
22	21	21	20	20	19	17	17	17	20

Hypotheses are,

  $\begin{array}{l}{H}_0:\mu =20\hfill \\ H_1:\mu <20\hfill \end{array}$

Lamar tests 40 different random cookies. And test the hypothesis using 95% confidence interval.

Lamar collects the data for 40 random cookies. Here using excel functions "=average ()" for mean and "=stdev()" for standard deviation the information for finding 95% confidence interval is,

  $\overline{x}=18.9,s=1.27,n=40$

The 95% confidence interval for mean is,

  $\begin{array}{l}\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}=18.9\pm 1.96\cdot \frac{1.27}{\sqrt{40}}\\ \begin{array}{l}=18.9\pm 0.39\hfill \\ =\left(18.51,19.29\right)\hfill \end{array}\end{array}$

Since confidence interval does not contain 20 so, one can reject the null hypothesis. That is one can conclude that there were fewer than 20 chocolate chips.