Question

You decide to collect data on the most burning, controversial question currently facing America: What is the population proportion of people living in the United States have Vanilla as their favorite ice cream flavor? You randomly and independently poll 100 people living in the United States. You find that 20 of them prefer Vanilla ice cream to all other flavors. a. Are the assumptions satisfied? b. What is pˆ for your sample? c. Find the critical value for a 60% confidence interval. d. Write the formula for a 60% confidence interval. (Some things simplify nicely. You won’t lose points if you don’t simplify, but I’ll have a warm glow of math-teachersatisfaction if you do simplify as much as you can.) e. A vanilla-hating cynic says that the true percentage of people living in the United States who prefer Vanilla ice cream is actually 10%. Write the H0 and the Ha for a hypothesis test using your data. f. What is the z-score from your data? g. What is the P-value? h. What is the outcome of your hypothesis test? Write a conclusion.

Answer 1

a) Yes, the assumpiton are satisfied.

• The sample is random and independent.
• And sample size is > 30.
• Data has a normal distribution.

b) n=100, x=20

= x/n = 20/100 = 0.20

c) At = 1-0.6 = 0.4, the critical value,

_{d) 60% confidence interval:}

e) Null and alternative hypothesis:

f) z-score is:

g) p-value = 0.0009

h) p-value = 0.0009 < =0.4, so, we reject null hypothesis.

Conclusion:

There is enough evidence to claim that true percentage of people living in the United States who prefer Vanilla ice cream is different than 10%​, at = 0.4 significance level.