Question

Please give step by step explanations.

An ice-cream company wants to compare the number of people who enjoyed two different types of ice-cream, vanilla and matcha. The company sampled 164 people for vanilla ice-cream and 120 of them like it. Among another sample of 88 people, 32 of them do not like matcha ice-cream. Test if there is a statistically significant difference in the proportion of people that like these two ice-creams. The significant level is 10%. What is the P-Value for your hypothesis test? (Please write down your hypothesis and hypothesis testing steps.)

Question 49 options:

a) 0.0681

b) 0.1362

c) 0.0832

d) 0.1664

Answer 1

Answer---->> given that ,

Here z value probability calculate from standard normal distribution table.

An ice cream company wants to compare the number of peoples who enjoyed two different types of ice crime vanilla and matcha.

The company sapmled 164 people for Vanilla ice cream and 120 people like it .

Among other sample of 88 people for matcha , 32 people don't like matcha ice cream i.e. 56 people like matcha matcha ice cream

From above information for Vanilla ice cream,

n1 = 160 , x1 = 120

Sample proportion = p1hat = x1/n1 = 120/160 = 0.75

p1hat = 0.75

For matcha ice cream

n2 = 88 , x2 = 56

Sample Proportion = p2hat= x2/n2 = 56/88 = 0.64

p2hat= 0.64

Pooled proportion = p = x1+x2 / n1+n2

= (120 + 56 )/ ( 160+88)

p= 0.71

Null and alternative hypothesis as follows ,

H0 :- p1-p2 is equal to 0 Vs.

H1:- p1-p2 is not equal to zero

Test statistic : Under H0 ,

Z = (p1hat - p2hat)/sqrt(p*(1-p )*((1/n1)+(1/n2))

=(0.75-0.64)/ sqrt((0.71*0.29)*((1/160)+(1/88))

Z= 1.8266

p-value :-

P(|Z| > 1.8266 ) = 1- P(|Z| < 1.8266)

= 2 - 2 * P(Z < 1.8266)

= 2 - 2 * 0.9656

= 0.068

Therefore , p-value = 0.068

option a). 0.0681 is correct option .