Question

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

      Ho:μ=82.7Ho:μ=82.7
      Ha:μ>82.7Ha:μ>82.7

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
75.1	93.4	101	69.5	74.1
114.1	106.4	78.9	116.3	87.3
92.5	80.6	59.6	70.8	79.8
94.4	90.3	78	102.4	105.5
95.9	77.1	108.4	75.6	74.6
112.4	58.1	90.3	70.8	112.4
100.4	101.7	83.6	65.9	82.8
86.5	86.1	77.5	81.5	58.1
84	97.4	85.3	77.1	86.5
78.5	64.1	79.8	54.2	84.4
114.1	81.5	64.1	72.5	68.8
51.4	89.4	95.4	65.9	95.4

Note: To save vertical scrolling space, the data set is shown here with five columns. In Statcrunch, you will need to make sure all the data are in ONE column.

Use Technology
What is the test statistic for this sample?
test statistic =  (Report answer accurate to 4 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

Answer 1

From the given data

Test Statistic:

t = (sample mean - population mean) / (SD / sqrt(n))

= (84.33 - 82.7) / (16/sqrt(60))

=0.7867

Answer: Test Statistic t = 0.7867

Using the P-value approach: The p-value is p = 0.2173 and since p = 0.2173 greater than 0.10, it is concluded that the null hypothesis is not rejected.

Thus we conclude that population mean is 82.7