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 408.0 grams, is there sufficient evidence at the 0.1 level that the bags are underfilled? Assume the standard deviation is known to be 20.0.

Step one: Enter the hypotheses:

H0:

Ha:

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

Step three: Specify if the test is one-tailed or two-tailed.

Step four: Enter the decision rule.

Reject H0 if z < _____

Step five: Enter the conclusion.

a. Reject Null Hypothesis

b. Fail to Reject Null Hypothesis

Answer 1

Solution :

Given that,

Population mean = = 410

Sample mean = = 408

Population standard deviation = = 20

Sample size = n = 46

Level of significance = = 0.01

Step one:

Claim : The bags are underfilled.

The null and alternative hypothesis is,  

Ho: 410

Ha: 410

Step two:

The test statistics,

Z =( - )/ (/n)

= ( 408 - 410 ) / ( 20 / 46 )

= -0.68

Step three:

This is a left (One) tailed test,

Step four:

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= -1.28

Reject H0 if z < -1.28

Step five:

Since it is observed that z = -0.68 = -1.28, it is then concluded that the null hypothesis is fail to reject.

b. Fail to Reject Null Hypothesis.