Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.005 . H o : μ = 50.1 H 1 : μ < 50.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 33.4 ,33.8, 47.5, 33.4, 57.7, 54.2

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) α

-greater than α

This p-value 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 50.1.

-There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 50.1.

-The sample data support the claim that the population mean is less than 50.1.

-There is not sufficient sample evidence to support the claim that the population mean is less than 50.1.

Answer 1

We are to test for population mean when population standard deviation is unknown.
Hwnce we will use one sample t test.
Test statistics is given by:

Hence test statistics t can be compted as

p-value for this test is
( from t distribution table with df=5 )
-fail to reject the null

option 4:  There is not sufficient sample evidence to support the claim that the population mean is less than 50.1.

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(33.4 – 43.333)2 + + (54.2 - 43.333)2 sample standard deviation s = (xi - x) = = 11.225625446569 WI 5

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