Question

2 The data given below show the number of overtime hours worked in one week per employee. Use the data to complete parts (a) and (b) Overtime hours 1 3 4 5 6 Employees 8 13 29 57 43 28 18 (6) Construct a probability distribution b) Graph the probability distribution using a histogram and describe its shape (a) Construct the probability distribution by completing the table below. 1 2 3 4 5 0 PE (Round to three decimal places as needed.) 1) Choose the correct graph of the probability distribution ОА. OB Ос. OD @ 04 03 02 03 02- 0.1 03 02 1 03 0.2- 012345 Overtime Hours 01333 Describe the distribution's shape. Choose the correct answer below OOO O approximately symmetric (but not uniform) skewed lo uniform Click to select your answertel

Answer 1

Question 1:

a)

Overtime hours	Employees	Probability
0	8	8/196 = 0.041
1	13	13/196 = 0.066
2	29	29/196 = 0.148
3	57	57/196 = 0.291
4	43	43/196 = 0.219
5	28	28/196 = 0.143
6	18	18/196 = 0.092
Total	196	1

b)

ANSWER: D

.

Histogram 0.35 0.30 0.25 0.20 Probability 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 Axis Title

ANSWER: A

A. approximately symmetric (but not uniform)

Question 2:

$\alpha$ = 0.01

Hypothesis:

$Ho: \mu_{1} = \mu_{2}$

$Ha: \mu_{1} \neq \mu_{2}$

Test statistic:

$Z = \frac{(\bar{X1} - \bar{X2})}{\sqrt{\frac{\sigma 1^2}{n1} + \frac{\sigma 2^2}{n2}}} = \frac{(17 - 15)}{\sqrt{\frac{3.6^2}{30} + \frac{1.4^2}{28}}} =2.82$

P-value = 0.0048 ....................Using Standrad Normal table

Conclusion:

P-value < $\alpha$ , i.e. 0.0048 < 0.01, That is Reject Ho at 1% level of significance.

ANSWER: C

C. Reject Ho, There is enough evidence at the 1% level of significance to reject the claim.

Question 3:

Hypothesis:

ANSWER: F

$Ho: \mu \leq 1220$

$Ha: \mu > 1220$

Test statistic:

$Z = \frac{\bar{X} - \mu }{\sigma /\sqrt{n}} = \frac{1237 - 1220}{212.52 /\sqrt{200}} = 1.13$

P-value = 0.129 .................Using standard Normal table

Conclusion:

P-value > $\alpha$ , i.e. 0.129 > 0.03, That is Fail to Reject Ho at 3% level of significance.

Reject Ho, At the 3% significance level, there is enough evidence to Reject the claim.