Question

A cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled. Each box of cereal is supposed to contain 13 ounces of cereal. A random sample of 36 boxes is tested. The sample average weight is 12.85 ounces and the sample standard deviation is 0.75 ounces. Use the critical-value approach to test whether the population average weight of a cereal box differs from 13 ounces. The critical-value should be:

Answer 1

Answer:

We conclude that the population average weight of a cereal box is equal to 13 ounces.

Step-by-step explanation:

We are given that a cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled.

A random sample of 36 boxes is tested. The sample average weight is 12.85 ounces and the sample standard deviation is 0.75 ounces.

Let $\mu$ = population average weight of a cereal box

So, Null Hypothesis, $H_0$ : $\mu$ = 13 ounces    {means that the population average weight of a cereal box is equal to 13 ounces}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ 13 ounces    {means that the population average weight of a cereal box differs from 13 ounces}

The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;

                                  T.S.  = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$  ~ $t_n_-_1$

where, $\bar X$ = sample average weight = 12.85 ounces

            $\sigma$ = sample standard deviation = 0.75 ounces

            n = sample of boxes = 36

So, test statistics  =  $\frac{12.85-13}{\frac{0.75}{\sqrt{36} } }$  ~ $t_3_5$

                               =  -1.20

The value of the test statistics is -1.20.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the t table gives critical values between -2.03 and 2.03 at 35 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population average weight of a cereal box is equal to 13 ounces.