Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410.0 gram setting. Based on a 46 bag sample where the mean is 412.0 grams, is there sufficient evidence at the 0.1 level that the bags are overfilled? Assume the standard deviation is known to be 20.0.

Step 1 of 5:

Enter the hypotheses:

Step 2 of 5:

Enter the value of the z test statistic. Round your answer to two decimal places.

Step 3 of 5:

Specify if the test is one-tailed or two-tailed.

Step 4 of 5:

Enter the decision rule.

Step 5 of 5:

Enter the conclusion.

Answer 1

Solution :

Given that,

Population mean = = 410

Sample mean = = 412

Population standard deviation = = 20

Sample size = n = 46

Level of significance = = 0.1

1)

The null and alternative hypothesis is,

Ho: 410

Ha: 410

2)

The test statistics,

Z =( - )/ (/n)

= ( 412 - 410 ) / 20 / 20

= 0.68

3)

This is a two tailed test.

4)

Critical value of  the significance level is α = 0.1, and the critical value for a two-tailed test is

= 1.64

| Z | > 1.64

5)

Since it is observed that |z| = 0.68 < = 1.64, it is then concluded that the null hypothesis is fail to reject.

Conclusion :

It is concluded that the null hypothesis Ho is fail to reject. Therefore, there is no enough evidence to claim that A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410.0 gram setting, at the 0.1 significance level.