Question

There were 13 that landed on their bases.

4. Using your same data again from your 50 tosses, test the claim that the population proportion of Kisses® chocolates that land completely on the base is less than 35% at α = 5% level of significance. a. State the null and alternate hypotheses. Identify the claim. b. State the level of significance. c. Determine the standardized test statistic. (2 decimal places) d. Calculate the P-value. (4 decimal places) e. Make a decision to “reject the

5. Will your decision in problem #4 change if you test at α = 10% level of significance?

Answer 1

a.

H0: The population proportion of Kisses chocolates that land completely on the base is greater or equal to 35%. That is, p 0.35.

H1: The population proportion of Kisses chocolates that land completely on the base is less than 35%. That is, p < 0.35.

The claim is the population proportion of Kisses chocolates that land completely on the base is less than 35%.

b.

Level of significance = 5% = 0.05

c.

Sample proportion, = 13/50 = 0.26

Standard error of sample proportion, SE = = 0.06745369

Standardized test statistic, z = ( - p) / SE = (0.26 - 0.35) / 0.06745369

= -1.33

d.

P-value = P(z < -1.33) = 0.0918

e.

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that the population proportion of Kisses chocolates that land completely on the base is less than 35%.

5.

When α = 10% level of significance,

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is strong evidence that the population proportion of Kisses chocolates that land completely on the base is less than 35%.