Question

You wish to test the following claim (H1) at a significance level of α=0.02.

      Ho:μ=52.5
      H1:μ<52.5

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

data
12.7
27.2
1.3

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 52.5.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 52.5.
• The sample data support the claim that the population mean is less than 52.5.
• There is not sufficient sample evidence to support the claim that the population mean is less than 52.5.

Please explain how to solve on a TI-84 if possible. Thanks!

Answer 1

Sol:

From Excel

using average function

and standard deviation we get sample mean and sample std dev

	data
	12.7
	27.2
	1.3
sample mean	13.73333
sample standard deviation	12.98088

Use TI 84 cal now

TESTS>T TEST>DATA and enter the data

You will get

test statistic =-5.173

p=0.0177

alpha=0.02 given

p<alpha

• less than α
• reject the null

There is sufficient evidence at 2% level of significance to conclude that :μ<52.5

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 52.5.