Question

Workers at a certain soda drink factory collected data on the volumes​ (in ounces) of a simple random sample of 15 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 ​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 11.95oz and 12.67​oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.18 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.18 oz. Use a 0.025 significance level. Complete parts​ (a) through​ (d) below.

Answer 1

Here we have given that

X: The volumes (in Ounces) of the cans of the soda drink

The X follows the normal distribution.

n=Number of cans of the soda drink=15

= sample mean = 12.19 oz

s= sample standard deviation=0.14 oz

Claim: To check whether the population of volumes has a standard deviation less than 0.18 oz.

The null and alternative hypothesis are

oz

v/s

oz

This is left one-tailed test.

Now, we can find the test statistic is as follows,

=

=8.47

The test statistics is 8.47

Now, we can find the p-value

Degrees of freedom = n-1 = 15-1 =14

p-value=

= 1- as this is left one tailed test

= 1- 0.8634 Using EXCEL=CHIDIST(, D.F=14)

=0.1366

we get the P-value=0.1366

Decision:

= level of significance=0.025

Here,

p-value (0.1366) > 0.025()

Conclusion:

We fail to reject the Null hypothesis Ho

we can conclude that there is not sufficient evidence to support the claim the population of volumes has a standard deviation less than 0.18 oz.