Answer to Question #115006 in Statistics and Probability for Katenda

Question

MMA tests the hypothesis that the average nbr of FNP is more than 4. Consider this to help carry out the test. n=30, x̅=5.5, σ=3 and a=0.01. Answer Q 12 to 16

Q 12
The correct set of hypothesis is
1. Ho : μ = 4; H1 : μ ≠ 4
2. Ho : μ = 5.5; H1 : μ ≠ 5.5
3. Ho : μ = 4; H1 : μ > 4
4. Ho : μ = 5.5; H1 : μ > 5.5
5. Ho : X = 4; H1 : X > 4

Q 13
The applicable test statistic is
1. Z test
2. t test
3. Chi–Square test
4. F–test

Q 14
The value of the test statistic and the critical value are
1. 1.5 and 2.33
2. 2.74 and 2.33
3. 2.74 and 2.58
4. 1.5 and 2.58

Q 15
The p-value for the test is
1. 0.0062
2. 0.0668
3. 0.1336
4. 0.0031

Q 16
What decision and conclusion can we take with regard to the hypothesis test
1. Reject null hypothesis(NH) and conclude that the average nbr of FNP > 4
2. Reject NH and conclude that the average nbr of FNP = 4
3. Don't eject NH and conclude that the average nbr of FNP = 4
4. Accept the NH

Answer 1

Q 12

The correct set of hypothesis is 

3. Ho : μ = 4; H1 : μ > 4 

Q 13

The applicable test statistic is

1. Z test 

Q 14

The value of the test statistic and the critical value are 

$$z_c=z_{1-\alpha}=2.33$$

$$z={\bar{x}-\mu\over \sigma/\sqrt{n}}={5.5-4\over 3/\sqrt{30}}\approx2.7386$$

2. 2.74 and 2.33 

Q 15

The p-value for the test is $p=0.003085<0.01$

4. 0.0031 

Q 16

What decision and conclusion can we take with regard to the hypothesis test 

Since $p=0.003085<0.01,$ it is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population mean $\mu$ is greater than 4, at the 0.01 significance level.

1. Reject null hypothesis(NH) and conclude that the average nbr of FNP > 4