A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 418 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 413 grams with a standard deviation of 20. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

No. At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the bags are underfilled (population mean significantly less than 418 g.)

Then, the null and alternative hypothesis are:

The significance level is 0.1.

The sample has a size n=9.

The sample mean is M=413.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.

The estimated standard error of the mean is computed using the formula:

Then, we can calculate the t-statistic as:

The degrees of freedom for this sample size are:

This test is a left-tailed test, with 8 degrees of freedom and t=-0.75, so the P-value for this test is calculated as (using a t-table):

As the P-value (0.237) is bigger than the significance level (0.1), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)

are ya tryin to ask something or is this a statement

ur right ive taken the test

step-by-step explanation: