Question

A survey determines that mint chocolate chip is the favorite ice cream flavor of 6% of consumers. An ice cream shop determines that of 190 customers, 15 customers stated their preference for mint chocolate chip. Find the P-value that would be used to determine if the percentage of customers who prefer mint chocolate chip ice has increased at a 5% level of significance. P-value:

Answer 1

0.1356661

Explanation:

A survey determines that mint chocolate chip is the favorite ice cream flavor of 6% of consumers. An ice cream shop determines that of 190 customers, 15 customers stated their preference for mint chocolate chip. Therefore, the P-value that would be used to determine if the percentage of customers who prefer mint chocolate chip ice has increased at a 5% level of significance is 0.1356661.

Answer 2

Answer: 0.1356661

Explanation:

Let p be the population proportion.

By the given information, we have

Null Hypothesis:
`H_0: p=0.06`

Alternative Hypothesis :
`H_1: p>0.06`

Since , the alternative hypothesis is right-tailed , then the test is a right -tailed test.

Given : Sample size : n= 190

Number of customers stated their preference for mint chocolate chip : 15

The , the sample proportion :
`\hat{p}=(15)/(190)\approx0.079`

Test statistic for proportion:

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

i.e
`z=\frac{0.079-0.06}{\sqrt{(0.06\cdot0.94)/(190)}}\approx1.10`

By using the standard normal distribution table for z-score , we have

P-value for right tailed test :
`P(Z>z)=1-P(Z<z)`

i.e.
`P(Z>1.10)=1-P(Z<1.10)=1-0.8643339=0.1356661`