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A politician claims that he is supported by a clear majority of voters. In a recent survey, 38 out of 60 randomly selected voters indicated that they would vote for the politician. (You may find it useful to reference the z table.)

a. Select the null and the alternative hypotheses.

multiple choice 1
H0: p = 0.50; HA: p ≠ 0.50
H0: p ≤ 0.50; HA: p > 0.50
H0: p ≥ 0.50; HA: p < 0.50


b. Calculate the sample proportion. (Round your answer to 2 decimal places.)



c. Calculate the value of test statistic. (Round final answer to 2 decimal places.)



d. Find the p-value.

multiple choice 2
0.025 p-value < 0.05
0.05 p-value < 0.10
p-value 0.10
p-value < 0.01
0.01 p-value < 0.025


e. At the 5% level of significance, what is the conclusion?

multiple choice 3
Do not reject H0; the politician’s claim is not supported by the data.
Do not reject H0; the politician’s claim is supported by the data.
Reject H0; the politician’s claim is not supported by the data.
Reject H0; the politician’s claim is supported by the data.

Respuesta :

Testing the hypothesis for the proportion, it is found that:

a) H0: p ≤ 0.50; HA: p > 0.50

b) The sample proportion is [tex]\pi = 0.6333[/tex].

c) The test statistic is [tex]z = 2.07[/tex].

d) The p-value of the test is of 0.0192.

e) Reject H0; the politician’s claim is supported by the data.

Item a:

At the null hypothesis, we test that the politician does not have the majority, thus:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, we test that he/she does have the majority, thus:

[tex]H_1: p > 0.5[/tex]

Item b:

38 out of 60, thus:

[tex]\pi = \frac{38}{60} = 0.6333[/tex]

The sample proportion is [tex]\pi = 0.6333[/tex].

Item c:

The test statistic is:

[tex]z = \frac{\pi - p}{\sqrt{\frac{p(1 - p)}{n}}}[/tex]

For this problem, [tex]\pi = 0.6333, p = 0.5, n = 60[/tex], thus:

[tex]z = \frac{0.6333 - 0.5}{\sqrt{\frac{0.5(0.5)}{60}}}[/tex]

[tex]z = 2.07[/tex]

The test statistic is [tex]z = 2.07[/tex].

Item d:

The p-value of the test is the probability of finding a sample proportion above 0.6333, which is 1 subtracted by the p-value of z = 2.07.

Looking at the z-table, z = 2.07 has a p-value of 0.9808.

1 - 0.9808 = 0.0192

The p-value of the test is of 0.0192.

Item e:

The p-value of the test is of 0.0192 < 0.05, thus, his claim is supported by the data, and we reject the null hypothesis. Then, the correct option is:

Reject H0; the politician’s claim is supported by the data.

A similar problem is given at https://brainly.com/question/24166849

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