Question

A researcher is interested in determining if the more than two thirds of students would support making the Tuesday before Thanksgiving a holiday. The researcher asks 1,000 random selected students if they would support making the Tuesday before Thanksgiving a holiday. Seven hundred students said that they would support the extra holiday. What is the null and alternative hypothesis?

Answer 1

Answer:

The null hypothesis is, {H₀}: p = 0.66, H₀: p = 0.66 .

The alternative hypothesis is, {Hₐ}: p > 0.66, Hₐ​: p > 0.66

Step-by-step explanation:

Let p represent the proportion of students who are supportive of making the day before Thanksgiving a holiday.

Since two populations are considered, the alternative hypothesis for the difference of the means of the two populations has to be stated.

The proportion of two-third students are supportive of making the day before Thanksgiving a holiday is p = 0.66 obtained as shown below:

The null hypothesis is,

{H₀}:p = 0.66, H₀​: p = 0.66

The alternative hypothesis is,

{Hₐ:p > 0.66, Ha​: p > 0.66

The null hypothesis is, {H₀}: p = 0.66, H₀: p=0.66 .

The alternative hypothesis is, {Hₐ}: p > 0.66, Hₐ​: p > 0.66

Answer 2

Using hypothesis concepts, it is found that:

The null hypothesis is $H_0: p \leq \frac{2}{3}$

The alternative hypothesis is: $H_1: p > \frac{2}{3}$

Basically, the null and alternative hypothesis are inverse, and they depend on what we want to test.

A researcher is interested in determining if the more than two thirds of students would support making the Tuesday before Thanksgiving a holiday.

Thus, at the null hypothesis, we test if the proportion is of at most two thirds, that is:

$H_0: p \leq \frac{2}{3}$

At the alternative hypothesis, we test if there is enough evidence to conclude if this proportion is more than two-thirds, that is:

$H_1: p > \frac{2}{3}$

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