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5. Chris claims that the average weight of tears shed by each student after an exam is more than 30 grams. You ask 42 random
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Answer #1

Ans 5)

Null Hypothesis states that the average weight of tears shed by each student after an is:

H_{o}:\mu = 30

Alternate Hypothesis states that the average weight of tears shed by each student after an is more than:

H_{a}:\mu > 30

Sample size n = 42

Sample mean \bar{x} = 30.3

Population\: standard\: deviation\: \sigma = 1

Significance level \alpha = 0.1

Since the population standard deviation is known we will do z-test

Test statistics:

z = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}

= \frac{30.3-30}{\frac{1}{\sqrt{42}}}

=1.94

Test statistics z = 1.94

Based on rejection region: The critical value for rejection region is z_{1-0.1} = 1.282

Since, z > zc (Reject Null Hypothesis.)

Based on P-value: P-value is 0.0262 Since, P-value < \alpha (Reject Null Hypothesis.)

Conclusion: Yes, there is enough evidence to conclude that the average weight of tears shed by each student after an is more than 30 grams.

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