In: Math

A researcher claims that the mean age of the residents of a small town is more than 32 years. The ages (in years) of a random sample of 36 residents are listed below. At α=0.10, α = 0.10 , alpha equals , 0.10 , comma is there enough evidence to support the researcher's claim? Assume the population standard deviation is 9 years. 41,33,47,31,26,39,19,25,23,31,39,36,41,28,33,41,44,40,30,29,46,42,53,21,29,43,46,39,35,33,42,35,43,35,24,21

From the given data, mean of the sample = 35.083 years. Since population standard deviation is given, we use the same to calculate the test statistic.

= 32 years, = 35.083 years, = 9 years, n = 36, = 0.10

**The
Hypothesis:**

H0: = 32

Ha: > 32

This is a right tailed Test.

**The Test
Statistic:** The test statistic is given by the
equation:

**The p Value:**
The p value (Right Tail) for Z = 2.06, is;
**p value = 0.0197**

**The Critical
Value:** The critical value (Right Tail) at
= 0.10, **Zcritical** **= +**1.282

**The Decision
Rule:** If Zobserved is > Zcritical, then Reject H0

Also if P value is < , Then Reject H0.

**The
Decision:** Since Zobserved (2.06) is >
Zcritical (1.282), We Reject H0.

Also since P value (0.0197) is < (0.10) , We Reject H0.

**The
Conclusion:** There is sufficient evidence at the 90%
significance level to support the claim that the mean age of the
residents of a small town is more than 32 years.

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33
47
31
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19
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36
41
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30
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1. A small town has 5600 residents. The residents in the town
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