Question

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

      Ho:μ=66.2Ho:μ=66.2
      Ha:μ>66.2Ha:μ>66.2

You believe the population is normally distributed and you know the standard deviation is σ=11.3σ=11.3. You obtain a sample mean of M=69.2M=69.2 for a sample of size n=27n=27.

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 greater than 66.2.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.2.
• The sample data support the claim that the population mean is greater than 66.2.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 66.2

Answer 1

Solution :

Suppose we wish to test the following claim (Ha) at a significance level of α=0.01.

      Ho:μ=66.2 Vs Ha:μ>66.2

We have been given that the population is normally distributed and the standard deviation is σ=11.3. Suppose we have sample mean of M=69.2 for a sample of size n=27.

Observe that the population standard deviation ( σ ) known and hence we use Z test to test the claim about population mean ( μ ).

The formula for test Statistic in this case is given by ;

Here in our case, = 69.2,   = 66.2,   = 11.3 and n = 27.
And hence the test statistic for this sample
test statistic = 1.380.

Now the p-value in this case can be calculated as,

so we get,

Therefore the p-value for this sample
p-value = 0.0838.

The p-value is greater than α.

This test statistic leads to a decision to fail to reject the null ( H0 ).

As such, the final conclusion is that; there is not sufficient sample evidence to support the claim that the population mean is greater than 66.2