Question

You wish to test the following claim (HaHa) at a significance
level of α=0.02.

Ho:μ=63.1Ho

Ha:μ<63.1Ha

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=67 with
mean M=54.6 and a standard deviation of SD=20.4.

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 63.1.
- _____There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 63.1.
- _____The sample data support the claim that the population mean is less than 63.1.
- _____There is not sufficient sample evidence to support the claim that the population mean is less than 63.1.

Answer #1

Test statistics

t = ( M - ) / ( S / sqrt(n) )

= (54.6 - 63.1) / (20.4 / sqrt(67) )

= **-3.411**

From T table,

with test statistics -3.411 and df of 66,

p-value = **0.0006**

The p-value is **less than (or equal to
)**

This test statistics leads to decision to **reject the
null**

Conclusion -

**There is sufficient evidence to warrant rejection of the
claim that the population mean is less than 63.1.**

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