Question

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

      Ho:μ=73.2
      Ha:μ<73.2

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

Column A	Column B	Column C	Column D	Column E
71.3	63.5	54.4	82.2	69.3
64.4	69.7	50.8	63.5	73.8
93.5	55	74.6	83.3	71.3
80.1	56.2	61.7	48.1	55
89.5	73.4	65.6	89.5	61.3
41.5	94.8	76.4	68.1	75.9
76.8	72.2	60.8	66.1	92.3
70.9	46	64.8	63.1	72.6
68.5	54.4	79.6	60.3	36.7
55	39.4	53	70.5	47.1
75.1	52.3	79.6	86.4	88.6

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 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 73.2.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 73.2.
• The sample data support the claim that the population mean is less than 73.2.
• There is not sufficient sample evidence to support the claim that the population mean is less than 73.2.

Answer 1

using minitab>stat>basic stat> one sample t-test we have

One-Sample T: Column A

Test of μ = 73.2 vs < 73.2

Variable N Mean StDev SE Mean 95% Upper Bound T P
Column A 55 67.45 14.16 1.91 70.65 -3.01 0.0019

test statistic =-3.01

p value = 0.0019

The p-value is less than (or equal to) α

This test statistic leads to a decision to reject the null

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 73.2.