Question

You wish to test the following claim (HaHa) at a significance level of α=0.05

      Ho:μ=82.8
      Ha:μ≠82.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=101 with mean ¯x=81.2 and a standard deviation of s=9.6

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

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 82.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 82.8.
• The sample data support the claim that the population mean is not equal to 82.8.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 82.8.

Answer 1

Here since the population is normally distributed, but population standard deviation.is not known we should use One sample t-test here

Given n=101

Sample mean =81.2

Sample Standard deviation S= 9.6

Null Hypothesis :  H0:μ = 82.8
Alternate Hypothesis Ha:μ ≠ 82.8

t-test statistic = ( - μ) / (S / )

= (81.2 - 82.8) / (9.6 / )

= -1.6 / 0.955236

= -1.67498

Number of degrees of freedom = n - 1

= 101 - 1

= 100

The p-value for 100 degrees of freedom and for a t-score of -1.67498 for a two-tailed test = 0.0971

Given significance level α=0.05

The p-value is greater than the significance level α

Since the p-value is greater than the significance level α,  We fail to reject the Null Hypothesis Ho

So the This test statistic leads to a decision to fail to reject the null

So the final conclusion is

There is not sufficient sample evidence to support the claim that the population mean is not equal to 82.8.