Question

2. A public polling agency conducts a survey to determine the current consumer sentiment concerning the state of the economy. Last year's poll shows that 30% of consumers are optimistic about the state of the economy. Suppose the public polling agency randomly samples 485 consumers and finds that only 158 are optimistic about the state of the economy.

a) What is the parameter of interest? explain

b) Construct a 95% confidence interval for the parameter of interest and interpret the confidence intervals.

c) Set up the null and alternative hypotheses for testing whether the current consumer sentiment concerning the state of the economy is different from the last year. (α = 0.05)

d) Sketch a graph and mark the rejection region.

e) Calculate the test statistic value.

f) Make the decision according to the rejection region approach.

g) Give the conclusion base on your decision

Answer 1

n= 485, x=158, p=30% = 0.30

a)

Parameter of interest is Population proportion ( P ) of consumers who are optimistic about the state of the economy.

b)

c= 95%

formula for confidence interval is

Where Zc is the z critical value for c= 95%

Zc= 1.96

0.28406 < P < 0.36748

We get 95% confidence interval as ( 0.284 ,  0.367)

c)

Ho: p = 0.30

Ha: p 0.30

d)

find z critical value for two tailed test with = 0.05

we get

Critical values are = ( -1.96 , 1.96 )

e)

formula for test statistics is

z = 1.239

test statistics= 1.24

f)

here test statistics (z = 1.24) do not lie in rejection region

hence we can say,

Null hypothesis (Ho) is NOT rejected.

g)

Therefore there is NOT sufficient evidence to conclude that the onsumer sentiment concerning the state of the economy is different from the last year.