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

Answer: 0.1356661

Step-by-step 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 : $\hat{p}=\dfrac{15}{190}\approx0.079$

Test statistic for proportion:

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

i.e  $z=\dfrac{0.079-0.06}{\sqrt{\dfrac{0.06\cdot0.94}{190}}}\approx1.10$

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. $P(Z>1.10)=1-P(Z<1.10)=1-0.8643339=0.1356661$

Answer 2

Answer:

0.1356661

Step-by-step 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.