Question

Seventy-three percent of a sample of 400 customers surveyed had a favourable impression of a new product (a) Estimate the value of the proportion of the population of all customers who have a favourable view of the new product (b) Compute and interpret the standard error of the sample proportion. (c) Determine a 95% confidence interval for the proportion of the population of customers who view the new product favourably (d) Interpret your results in part (c). (e) Using the same survey data, test the hypothesis that the population proportion with a favourable view of the new product is at least 0.70. Use the 0.05 level of significance (f) What is the relationship between confidence intervals and hypothesis tests?

Answer 1

Answer)

A)

P = 0.73

N = sample size = 400

Value of the proportion = n*p = 400*0.73 = 292

B)

Standard error = √p*(1-p)/√n

= √{0.73*(1-0.73)}/√400

Standard error = 0.0221979728804

C)

First we need to check the conditions of normality

That is if n*p and n*(1-p) both are greater than 5 or not

N*p = 292 > 5

N*(1-p) = 108 > 5

As both the conditions are met, we can use standard normal z table to estimate the interval

From z table, critical value z for 95% confidence level is 1.96.

Margin of error = z*standard error = 1.96*0.0221979728804

MOE = 0.0435080268456

Confidence interval is given by,

(P-MOE, P+MOE)

(0.6864919731543, 0.7735080268456)

D)

We are 95% confident that true population proportion lies in the interval (0.686, 0.774)