The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of the consumers like it. A random sample of 300 consumers was surveyed, and 84 respondents indicated that they liked the campaign, equivalent to 28%. What are the null and alternative hypothesis? If the test-statistic is calculated to be -0.7407, at significance level of 5% with critical value of 1.64, can we reject the null and say we should the campaign be changed?

The null and alternative hypotheses are;

Null hypothesis; H0: p ≥ 0.3

Alternative hypothesis; Ha: p < 0.3

The conclusion of the hypotheses is that; We reject the null hypothesis and conclude that;

The current advertising campaign for the major soft drink brand should be changed.

We are given;

Population proportion; p' = 30% = 0.3

Sample proportion; p = 28% = 0.28

Sample size; n = 300

Thus;

Null hypothesis; H0: p ≥ 0.3

Alternative hypothesis; Ha: p < 0.3

z = (p' - p)/(√(p(1 - p)/n)

This means that our calculated z-score falls to the left of the rejection region and as such we will reject the null hypothesis and conclude that;

The current advertising campaign for the major soft drink brand should be changed.

Read more on hypotheses testing at;link

|Z| = | -0.747 | = 0.747 < 1.64 at 5% level of significance

Null Hypothesis is accepted at 5% level of significance

The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of the consumers like it and not be changed

Step-by-step explanation:

Step(i):-

Given Population proportion P = 30 percentage

                                             P = 0.30

sample proportion

Null Hypothesis :-

P = 0.30

Alternative Hypothesis:-

P ≠ 0.30

Step(ii):-

Test statistic

                 Z = -0.747

|Z| = | -0.747 | = 0.747

tabulated value   Z =  1.64 at 5% level of significance

|Z| = | -0.747 | = 0.747 < 1.64 at 5% level of significance

Null Hypothesis is accepted at 5% level of significance

The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of the consumers like it.

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

2.83941151 would be the answer you're looking for! : )