Question

It is believed 30% of a city's population is interested in a new shopping center. A developer wants to know if this value is accurate. She commisions a survey of 407 people and finds that 140 are interested in a new shopping center. At the .05 significance level, conduct a full and appropriate hypothesis test for the developer.

a) What are the appropriate null and alternative hypotheses?

A		H0:p^=.3H1:p^<.3
B		H0:p^=.3H1:p^>.3
C		H0:p=.3H1:p<.3
D		H0:p^=.3H1:p^=.3
E		H0:p=.3H1:p>.3
F		H0:p=.3H1:p≠.3

b) Identify the other values given in the problem:

1) = 407

2) = 140

3) = .05

c) Calculate the value of the test statistic.  Round your response to at least 2 decimal places.

d) What is the corresponding P-value for the test statistic? Round your response to at least 4 decimal places.

e) Make a decision: Since α (<, >, =) P, we (reject, accept) the null hypothesis (H0, H1)

d) Help write a summary of the results of this hypothesis test:

(There is, there is not, we do not whether there is) enough evidence in this sample to conclude the proportion of (Austin's population, men, people, the city's population, women)

who are interested in a new shopping center is (different from, less than, greater than) .3 at the α= (.05, .1, .01) significance level because  P= (?)

Answer 1

Ans:

a)

H0:p=.3

H1:p≠.3

b)

n=407

x=140

alpha=0.05

c)

sample proportion=x/n=140/407=0.3440

Test statistic:

z=(0.3440-0.30)/sqrt(0.3*(1-0.3)/407)

z=1.936

d)

p-value=2*P(z>1.936)=2*0.0264=0.0528

e)As,alpha<p-value,we accept the null hypothesis.

d)

There is not enough evidence in this sample to conclude the proportion of the city's population, who are interested in a new shopping center is different from .3 at the α= .05 significance level because  P= 0.0528