Question

A car manufacturer claims that 52% of Americans are interested in having internet access in their cars. In a simple random sample of 300 Americans, 161 stated they were interested in having web access in their cars. Test the hypothesis that more than 52% of Americans are interested in having internet access in their cars. Assume independence. Use .05 as the level of significance.

Complete the steps below:

a) Write the null and alternative hypotheses using proper notation.

b) Explain how each of the conditions of CLT are met.

c) Give the z-test statistic AND the p-value.

d) Using your p-value, what is your decision about the null hypothesis.

e) What is your conclusion regarding whether or not more than 52% of Americans are interested in having web access in their cars? Be sure to use the phrase statistically significant.  

Answer 1

Ans:

a)

b)sample is random and independent.

300*0.52*(1-0.52)=74.88>10

Yes,all condistions are met.

c)

sample proportion=161/300=0.5367

Test statistic:

z=(0.5367-0.52)/sqrt(0.52*(1-0.52)/300)

z=0.578

p-value=P(z>0.578)=0.2816

d)As,p-value>0.05,we fail to reject the null hypothesis.

e)There is not sufficient evidence to conclude that more than 52% of Americans are interested in having web access in their cars.