Question

out of a sample of 1031 Americans surveyed, 912 of them own a television

a) is there a significant evidence at a=0.05 to conclude the majority of Americans (>50%) own a television?

i) verify the normality condition necessary for the hypothesis testing.

ii) step 1: Ho:________ H1: ______________

iii) step 2: a=________

iv) step 3: calculate test statistic:

v) now, use your calculator to find the p-value.

vi) are you going to reject or fail to reject the hypothesis claim?

vii) state your conclusion based on the hypothesis statement above

viii) what time of error could you have made in part a? type _________ error.

b) construct the 95% confidence intervals for the proportion of all television owners in america assuming the sample size is large enough

c) what would be the required sample size if one would like to estimate the proportion of television owners within 0.02 (E=0.02) at a=0.1

Answer 1

(i) Normality condition is

we have p = 912/1031 = 0.88

and n = 1031

so, np = 0.88*1031 = 907.28

and n(1-p) = 1031*(1-0.88) = 123.72

so, conditions of normality met

(ii) Ho: p = 0.50, H1:

(iii)

(iv) Calculation for test statistic

z =

setting

we get

z =

(v) P value from z value

P(z>24.40) = 1 - P(z<24.40) = 1 - 1 = 0

(vi) we will reject null hypothesis because p value is less than 0.05

(vii) we can conclude that we have enough evidence to support the claim that majority of americans own a television since p value is significant at 0.05 level