Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 409 gram setting. Based on a 21 bag sample where the mean is 417 grams and the standard deviation is 26, is there sufficient evidence at the 0.1 level that the bags are overfilled? Assume the population distribution is approximately normal.

Step 1 of 5:

State the null and alternative hypotheses.

Step 2 of 5:

Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5:

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

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5:

Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Given

= 409

= 417

s = 26

n = 21

1)

The null and alternative hypothesis is ,

H₀ :   = 409

H_a : > 409

2)

Test statistic = Z =

= ( - ) / (s / n)

= (417 - 409) / (26 / 21 )

= 8 / 5.67

Test statistic = Z = 1.41

degrees of freedom = n - 1 = 21 - 1 = 20

using t-table at Z = 1.41 = 0.9207

p(Z > 1.41) = 1-P (Z < 1.41)

= 1 - 0.9207

P-value = 0.0793

= 0.1

P-value <

3)

it is two tailed hypothesis test

4)

P-value <

0.079 <0.1

So, reject the null hypothesis .

5)

There is sufficient evidence to suggest that  the bags are overfilled.

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