Chapter PVI, Problem 32RE

(a)

To determine

To write appropriate hypothesis.

Answer to Problem 32RE

  $\begin{array}{l}{H}_0:\mu =35.4\\ H_a:\mu <35.4\end{array}$

Explanation of Solution

It is given in the question that as a project for an introductory statistics course, students checked six bags of Fritos marked with a net weight of $35.4$ grams. The given claim in the question is that the average less than $35.4$ grams. The null hypothesis states that the population mean is equal to the value mentioned in the claim. If the null hypothesis is the claim then the alternative hypothesis states the opposite of the null hypothesis. So, we have,

  $\begin{array}{l}{H}_0:\mu =35.4\\ H_a:\mu <35.4\end{array}$

(b)

To determine

To check the assumptions for inference.

Answer to Problem 32RE

All conditions are not satisfied.

Explanation of Solution

It is given in the question that as a project for an introductory statistics course, students checked six bags of Fritos marked with a net weight of $35.4$ grams. So, we have,

  $\begin{array}{l}{H}_0:\mu =35.4\\ H_a:\mu <35.4\end{array}$

Let us check the conditions and assumptions for inference as,

Random condition: It is satisfied as assuming that the sample is a random sample.

  $10\%$ condition: It is satisfied as the sample of six bags of Fritos is less than $10\%$ of all bags of Fritos.

Normal condition: It is not satisfied since the normal probability plot contains an outlier.

Thus, we note that all conditions are not satisfied.

(c)

To determine

To test your hypothesis using all six weights.

Answer to Problem 32RE

There is not sufficient evidence to support the claim that the mean weight of bags of Fritos is less than advertised.

Explanation of Solution

It is given in the question that as a project for an introductory statistics course, students checked six bags of Fritos marked with a net weight of $35.4$ grams. So, we have,

  $\begin{array}{l}{H}_0:\mu =35.4\\ H_a:\mu <35.4\end{array}$

Thus, to test the hypothesis for mean we will use the calculator $\text{TI}-89$ . In the STAT Tests menu, choose $2:$ T -Test. You must specify whether you are using data stored in a list or whether you will enter the mean, standard deviation, and size of your sample. You must also specify the hypothesized model mean and whether the test is to be two-tail, lower-tail, or upper-tail. Select whether the test is to be simply computed or whether to display the distribution curve and highlight the area corresponding to the P-value of the test.It is an lower tail test.

With the outlier, we have, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P>0.10\\ t=0.725\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude that there is not sufficient evidence to support the claim that the mean weight of bags of Fritos is less than advertised.

(d)

To determine

To retest your hypothesis with one unusually high weight removed.

Answer to Problem 32RE

There is not sufficient evidence to support the claim that the mean weight of bags of Fritos is less than advertised.

Explanation of Solution

It is given in the question that as a project for an introductory statistics course, students checked six bags of Fritos marked with a net weight of $35.4$ grams. So, we have,

  $\begin{array}{l}{H}_0:\mu =35.4\\ H_a:\mu <35.4\end{array}$

Thus, to test the hypothesis for mean we will use the calculator $\text{TI}-89$ . In the STAT Tests menu, choose $2:$ T -Test. You must specify whether you are using data stored in a list or whether you will enter the mean, standard deviation, and size of your sample. You must also specify the hypothesized model mean and whether the test is to be two-tail, lower-tail, or upper-tail. Select whether the test is to be simply computed or whether to display the distribution curve and highlight the area corresponding to the P-value of the test. It is an lower tail test.

Without the outlier, we have, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P>0.10\\ t=-0.535\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude that there is not sufficient evidence to support the claim that the mean weight of bags of Fritos is less than advertised.

(e)

To determine

To explain what would you conclude about the stated weight.

Explanation of Solution

It is given in the question that as a project for an introductory statistics course, students checked six bags of Fritos marked with a net weight of $35.4$ grams. So, we have,

  $\begin{array}{l}{H}_0:\mu =35.4\\ H_a:\mu <35.4\end{array}$

Thus, we conclude about the stated weight that there is not sufficient evidence to support the claim that mean weight of bags of Fritos is less than advertised.