Question

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

      Ho:μ=82.1Ho:μ=82.1
      Ha:μ>82.1Ha:μ>82.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=16n=16 with mean M=90.8M=90.8 and a standard deviation of SD=13.9SD=13.9.

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 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 greater than 82.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.1.
• The sample data support the claim that the population mean is greater than 82.1.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 82.1.

Answer 1

The null and alternatiev hypothesis is ,

(Claim)

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now df=degrees of freedom=n-1=16-1=15

The test statistic is ,

The p-value is ,

p-value= ; The Excel function is , =TDIST(2.5036,15,1)

The p-value is less than 0.05

This p-value leads to a decision to reject the null hypothesis.

Conclusion : There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 82.1.