A test of H0: p = 0.5 versus Ha: p > 0.5 has the test statistic z = 1.15. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is Ha: p ≠ 0.5, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points)

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22-04-2020
Mathematics

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A test of H0: p = 0.5 versus Ha: p > 0.5 has the test statistic z = 1.15. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is Ha: p ≠ 0.5, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points)

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mtosi17 mtosi17 · Answer 1 · 2020-04-24T02:38:55+02:00

Answer:

Part A: The null hypothesis failed to be rejected.

Part B: The null hypothesis failed to be rejected.

Step-by-step explanation:

We have an hypothesis test with null and alternative hypothesis H0: p = 0.5 versus Ha: p > 0.5, which has the test statistic z=1.15.

Part A: If the significance level is 0.05, the conclusion depends on the P-value.

If the P-value is below 5%, the null hypothesis is rejected.

The P-value for this right-tailed tes and z=1.15 is:

[tex]P-value=P(z>1.15)=0.125[/tex]

The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.

Part B: In this case, the significance level is 0.01 and, as the alternative hypothesis is defined with an unequal sign, the test is two-tailed.

This changes the way we calculate the P-value, as we need to compute the two tails.

The P-value is:

[tex]P-value=2P(z>1.15)=0.25[/tex]

The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-01-11T10:39:13+01:00

Null hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable. The null hypothesis is failed to be rejected for both part A and part B of the question.

Given-

Using the hypothesis test we have,

[tex]H_o; p=0.5[/tex]

[tex]H_ap>0.5[/tex]

[tex]z=1.15[/tex]

Null hypothesis

Null hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable.

Part A: The conclusion to draw at the 5% significance level-

In the right tailed test or upper test the p value for the z score can be given form z table which is,

p-value[tex]=0.125[/tex]

Here the p value 0.125 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.

Part B: If the alternative hypothesis is Ha: p ≠ 0.5, the conclusion to draw at the 5% significance level-

Here for the unequal sign 2-test is performed. The p value for the 2-test is,

p- value[tex]=0.25[/tex]

Here the p value 0.25 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.

Hence, the null hypothesis is failed to be rejected for both part A and part B of the question.

For more about the null hypothesis, follow the link below-

https://brainly.com/question/4454077