Question

A random sample of 250 households in a large city revealed that the mean number of televisions per household was 2.76 From previous analyses we know that the population standard deviation is 1.8.

a) State the appropriate hypotheses, if we wish to determine that the true mean number of televisions per household is at least 2.5.

b) Test the hypotheses at the 10% significance level and explain your conclusion.

Answer 1

Solution :

Given that ,

= 2.5

= 2.76

= 1.8

n = 250

The null and alternative hypothesis is ,

H₀ :   = 2.5

H_a :     2.5

This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 2.76 - 2.5) / 1.8 / 250

= 2.28

The test statistic = 2.28

P - value = P(Z > 2.28 ) = 1- P (Z < 2.28 )

= 1 - 0.9887

= 0.0113

P-value = 0.0113

= 0.10

0.0113 < 0.10

P-value <

Reject Ho.

Conclusion :- Reject the null hypothesis .There is sufficient evidence to test the claim.that the true mean number of televisions per household is at least 2.5.at the 10% significance level .