Question

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 students if you could collect their tears after an exam and find that the average weight was 30.3 grams. Assume the population standard deviation is 1 gram. At a = 0.1 is there enough evidence to support Chris' claim? 6. A researcher claims that the proportion of males who have tested positive for Covid-19 is less

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

Since, z > z_c (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.