Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 21 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.09 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.91 oz and 12.55 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.025 significance level. Complete parts (a) through (d) below. O B. Ho: a = 0.16 oz OA Hg: o20.16 oz H:o<0.16 oz H,: 0#0.16 oz OC. Ho: o=0.16 oz H,:o<0.16 oz O D. Ho: o>0.16 oz H,:0 = 0.16 oz b. Compute the test statistic. (Round to three decimal places as needed.) c. Find the P-value. P-value = (Round to four decimal places as needed.) d. State the conclusion. Hg, because the P-value is v the level of significance. There is evidence to conclude that the population standard deviation of can volumes is less than 0.16 oz.

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 21 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.09 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.91 oz and 12.55 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.025 significance level. Complete parts (a) through (d) below. O B. Ho: a = 0.16 oz OA Hg: o20.16 oz H:o<0.16 oz H,: 0#0.16 oz OC. Ho: o=0.16 oz H,:o<0.16 oz O D. Ho: o>0.16 oz H,:0 = 0.16 oz b. Compute the test statistic. (Round to three decimal places as needed.) c. Find the P-value. P-value = (Round to four decimal places as needed.) d. State the conclusion. Hg, because the P-value is v the level of significance. There is evidence to conclude that the population standard deviation of can volumes is less than 0.16 oz.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 21 cans of the soda drink. These volumes have a mean of 12.19 oz and a standard deviation of 0.09 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.91 oz and 12.55 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.025 significance level.

Complete parts (a) through (d) below:

**Options for Hypotheses:**

- **A.** $ H_0: \sigma = 0.16 \, \text{oz} $
$ H_1: \sigma < 0.16 \, \text{oz} $

- **B.** $ H_0: \sigma = 0.16 \, \text{oz} $
$ H_1: \sigma \neq 0.16 \, \text{oz} $

- **C.** $ H_0: \sigma = 0.16 \, \text{oz} $
$ H_1: \sigma < 0.16 \, \text{oz} $

- **D.** $ H_0: \sigma > 0.16 \, \text{oz} $
$ H_1: \sigma = 0.16 \, \text{oz} $

**b. Compute the test statistic.**

\[
\chi^2 = \, \_\_\_\_\_
\]

(Round to three decimal places as needed.)

**c. Find the P-value.**

P-value = $\ \_\_\_\_\_ $

(Round to four decimal places as needed.)

**d. State the conclusion.**

Reject $ H_0 $ because the P-value is $\ \_\_\_\_\_ $ the level of significance. There is $\ \_\_\_\_\_ $ evidence to conclude that the population standard deviation of can volumes is less than 0

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