Question

You wish to test the following claim (Ha) at a significance level of α=0.10.

      Ho:μ=68.4
      Ha:μ<68.4

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
95.9	71.8	55	90.9	53.6
76	71.3	73.3	67.2	69
59.3	65.1	59.7	74.9	70.8
51.7	54.1	85.3	76	71.8
69	53.6	66.8	66.4	56.8
62.6	57.6	52.6	50.1	89.2
71.8	45.9	76.6	59.3	49
100.4	31.4	61	66.4	45.9
31.4	50.1	64.7	42.9	42.9
59.7	81.5	66.4	90.9	71.3
62.6	56.8	72.8	67.7	45.2

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 68.4.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 68.4.
• The sample data support the claim that the population mean is less than 68.4.
• There is not sufficient sample evidence to support the claim that the population mean is less than 68.4.

Answer 1

The statistical software output for this problem is:

One sample T hypothesis test: V: Mean of variable Ho : = 68.4 HA: < 68.4 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat Data 64.218182 2.0016039 54 -2.0892336 P-value 0.0207

Hence,

Test statistic = -2.089

p - Value = 0.0207

less than (or equal to) α

Reject the null

Final conclusion: Option A is correct.