Question

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?

Answer 1

Answer:

|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

                        $p = \frac{84}{300} = 0.28$

Null Hypothesis :-

P = 0.30

Alternative Hypothesis:-

P ≠ 0.30

Step(ii):-

Test statistic

                    $Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

                   $Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } } = \frac{0.28-0.30}{\sqrt{\frac{0.28 X 0.30}{300} } }$

                 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.

Answer 2

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

• We are not given the standard deviation and so the formula for z-score here is;

z = (p' - p)/(√(p(1 - p)/n)

• We are told the test statistic is calculated as z = -0.7407

• This z-value is less than the critical value of 1.64.

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.

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