Question

A blind taste test is conducted to determine which of two colas, Brand A or Brand B, individuals prefer. Individuals are randomly asked to drink one of the two types of cola first, followed by the other cola, and then asked to disclose the drink they prefer. Results of the taste test indicate that 44 of 100 individuals profor Brand A Complete parts a through c. (a) Conduct a hypothesis test (proferably using technology) Ho: p=Po versus H :D? Do for Do = 0.33, 0.34, 0.35, ... 0.53,0.54, 0.55 at the a = 0.05 level of significance. For which values of Po do you not reject the null hypothesis? What do each of the values of Do represent? Do not reject the null hypothesis for the values of p, between and inclusively. (Type integers or decimals as needed.)

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Answer 1

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a) We will check this by finding the confidence interval.

n = 100, x = 44

p̅ = x/n = 0.44

95% Confidence interval :

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.44 - 1.96 *√(0.44*0.56/100) = 0.343

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.44 + 1.96 *√(0.44*0.56/100) = 0.537

0.343 < p < 0.537

As the value 0.33 is not in the interval so we will reject 0.33

As the value 0.34 is in the interval so we will not reject 0.34

The value 0.53 is included in the so we will not reject 0.53

As the value 0.54 is not in the interval so we will reject 0.54

Do not reject the null hypothesis for the values of p0 between 0.34 and 0.53, inclusively.