Question

You wish to test the following claim (H1H1) at a significance
level of α=0.01α=0.01.

Ho:μ=82.5Ho:μ=82.5

H1:μ≠82.5H1:μ≠82.5

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=449n=449
with mean M=81.7M=81.7 and a standard deviation of
SD=10.7SD=10.7.

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 not equal to 82.5.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 82.5.
- The sample data support the claim that the population mean is not equal to 82.5.
- There is not sufficient sample evidence to support the claim that the population mean is not equal to 82.5.

Answer #1

**Solution :**

The null and alternative hypothesis are

**H _{0} :
= 82.5 ......... Null hypothesis**

**H**_{a} **:
**
**82.5 .......... Alternative hypothesis**

Here, n = 449, = 81.7, s = 10.7

The test statistic t is,

t =

= [81.7 - 82.5]/[10.7 /449]

= -1.584

**The value of the test statistic t = -1.584**

Now ,

d.f. = n - 1 = 449 - 1 = 448

sign in Ha indicates that the test is TWO TAILED.

t = -1.584

So , using calculator ,

**p value = 0.1138**

Since,

p value is greater than the significance level 0.01 .

Decision: **Fail to Reject the null hypothesis
H0**

**Conclusion :**

**There is not sufficient evidence to warrant rejection of
the claim that the population mean is not equal to
82.5.**

You wish to test the following claim (H1H1) at a significance
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