Question

You wish to test the following claim (H1H1) at a significance
level of α=0.002α=0.002.

Ho:μ=51.3Ho:μ=51.3

H1:μ<51.3H1:μ<51.3

You believe the population is normally distributed, but you do not
know the standard deviation. You obtain a sample of size n=627n=627
with mean ¯x=49.8x¯=49.8 and a standard deviation of
s=8.9s=8.9.

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 51.3.
- There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 51.3.
- The sample data support the claim that the population mean is less than 51.3.
- There is not sufficient sample evidence to support the claim that the population mean is less than 51.3.

Answer #1

Solution :

This is the left tailed test,

The null and alternative hypothesis is ,

H_{0} :
= 51.3

H_{a} :
< 51.3

Test statistic = t =

= ( - ) / s / n

= (49.8 - 51.3) / 8.9 / 627

Test statistic = t = -4.220

degrees of freedom = n - 1 = 627 - 1 = 626

P(t < -4.220)

P-value = 0

α = 0.002.

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

This test statistic leads to a decision to reject the null

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 51.3

You wish to test the following claim (H1H1) at a significance
level of α=0.002α=0.002.
Ho:μ=63.9Ho:μ=63.9
H1:μ<63.9H1:μ<63.9
You believe the population is normally distributed, but you do not
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data
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79.7
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