Question

You wish to test the following claim (H1H1) at a significance
level of α=0.05α=0.05.

Ho:μ=67.1Ho:μ=67.1

H1:μ<67.1H1:μ<67.1

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=97n=97
with mean M=64.7M=64.7 and a standard deviation of
SD=14.1SD=14.1.

What is the test statistic for this sample? (Report answer accurate
to three decimal places.)

test statistic =

What is the p-value for this sample? (Report answer accurate to
four decimal places.)

p-value =

The p-value is...

- less than (or equal to) αα
- greater than αα

This test statistic leads to a decision to...

- reject the null
- accept the null
- fail to reject the null

As such, the final conclusion is that...

- There is sufficient evidence to warrant rejection of the claim that the population mean is less than 67.1.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 67.1.
- The sample data support the claim that the population mean is less than 67.1.
- There is not sufficient sample evidence to support the claim that the population mean is less than 67.1.

Answer #1

Solution :

Given that,

Population mean = = 67.1

Sample mean = = 64.7

Sample standard deviation = s = 14.1

Sample size = n = 97

Level of significance = = 0.05

This is a **left tailed** test.

The test statistics,

t = ( - )/ (s/)

=( 64.7 - 67.1) / ( 14.1/97)

**= -1.676**

**P- Value = 0.0485**

The p-value is **p = 0.0485 < 0.05**, it is
concluded that **reject the null hypothesis**.

Conclusion :

**There is sufficient evidence to warrant rejection of the
claim that the population mean is less than 67.1**

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level of α=0.05α=0.05.
Ho:μ=89.5Ho:μ=89.5
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You believe the population is normally distributed, but you do not
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