Question

The population is normally distributed. A sample produces the following observations:(You may find It useful to reference the appropriate table: z teble orttable 6 98 77 11 18 Click here for the Excel Data File a. Find the mean and the standard deviation. (Round your answers to 2 declmal places.) Mean Standard deviation b. Calculate the value of the test statistic. (Round Intermedlete calculetlons to at least 4 declmal places and final answer to 2 declmal places.) Test statistic c. Find the p-value. p-value < 0.01 0.01 s p-value < 0.02 0.02 s p-value< 0.05 0.05 s p-value < 0.10 p-value a 0.10 d. At the 5% significance level, what is the conclusion? OReject He since the p-value is greater than a. OReject Hg since the p-value is smaller than a O Do not reject He since the pvalue is greater than α.

Answer 1

(a)

(i) Sample mean = $\bar{x}$ = 58/7 = 8.2857

(ii)

x	x - $\bar{x}$	(x - $\bar{x}$ )2
6	- 2.2857	5.2245
9	0.7143	0.5102
8	- 0.2857	0.0816
7	- 1.2857	1.6530
7	- 1.2857	1.6530
11	2.7143	7.3673
10	1.7143	2.9388
Total =		19.4286

Sample SD (s) is given by:

$s=\sqrt{\frac{\sum_{i=1}^{7}(x_{i}-\bar{x})^{2}}{6}}=\sqrt{\frac{19.4286}{6}}=\sqrt{3.2381}=1.7995$

So,

Answer is:

Mean	8.2857
Standard deviation	1.7995

(b)

SE = s/ $\sqrt{n}$

= 1.7995/ $\sqrt{7}$

= 0.6801

Test statistic is:

t = (8.2857 - 8)/0.6801 = 0.5141

So, answer is:

Test statistic

0.51

(c)

t score = 0.51

ndf = 7 - 1 = 6

Two Tail Test

By Technology, p - value = 0.6255

So,

Correct option:

p - value > 0.10

(d)

Correct option:

Do not reject H0 since the p - value is greater than $\alpha$ .