Question

A random sample of 50 consumers taste-tested a new snack food. Their responses (where 0 do not like; 1 like; 2- indifferent) are reproduced below. Complete parts a and b below. 0 200 200 2 010 a. Test Ho: p-0.43 against Ha: p > 0.43, where p is the proportion of customers who do not like the snack food. Use Identify the test statistic, z. 0.43 (Round to two decimal places as needed.) Now identify the rejection region. Select the correct choice below and fill in the answer box to complete your choice. #005. Round to two decimal places as needed.) Ов.zs

Answer 1

The statistic is:

$z= \frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{}n}}$

where $\hat{p}$ is the sample proportion

$p_0$ is the proportion under the null hypohtesis(in this case p₀=0.43)

and n is the number of observations

In this case n=50 observations and since there are 23 zeros in the data, then the sample proportion is

$\hat{p}= \frac{23}{50}=0.46$

Therefore the test statistic is

$z= \frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{}n}}= \frac{0.46-0.43}{\sqrt{\frac{0.43(1-0.43)}{50}}}=0.42848$

The answer is z=0.43

We reject the null hypothesis if z is greater than the 95th percentile of a standard normal distribution

which is  1.64485

so the answer is

A. z>1.64

We don't reject the null hypothesis