A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is overfilling the bags. A 19 bag sample had a mean of 412 grams with a standard deviation of 15. Assume the population is normally distributed. Is there sufficient evidence at the 0.1 level that the bags are overfilled? Step 2 of 6: Find the value of the test statistic. Round your answer to three decimal places.

Answer:
Given:

The hypothesized mean (μ)=407
The sample mean (x)=412
The sample standard deviation (s)=15
The sample size (n)=19

The significance level (α)=0.1

Solution:
The null and alternative hypothesis:

H0:μ=407
Ha:μ>407

The test statistic (t):
t=xμsn

=4124071519

=1.453

The degree of freedom (df):
df=n1
=191
=18

The p-value:
The p-value=P(t>1.453)

=0.0817

The final conclusion:

The p-value is less than the significance level. Therefore, there is sufficient evidence to conclude that the bags are overfilled at the 0.1 significance level.

Final Answer:

The null and alternative hypothesis:

H0:μ=407
Ha:μ>407

The test statistic (t)=1.453

The p-value =0.0817

The final conclusion:

The p-value is less than the significance level. Therefore, there is sufficient evidence to conclude that the bags are overfilled at the 0.1 significance level.

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