Question

13% of people mind if others smoke near a building entrance. A researcher thinks it has decreased. a) Express the null and alternative hypotheses in symbolic form for this claim. Ho: H: Use the following codes to enter the following symbols: > enter> < enter <= # enter ! b) You decide to survey 100 adult Americans and find that 74 of people mind if others smoke near a building entrance. Find the test statistic. Round to two decimal places. c) What is the p-value? Round to 4 decimals. p = d) Make a decision base on a 0.05 significance level. Reject the null Do not reject the null

Answer 1

Solution :

Given that,

$p_{0}$ = 0.13

1 - $p_{0}$ = 0.87

n = 100

x = 74

Level of significance = $\alpha$ = 0.05

Point estimate = sample proportion = $\hat p$ = x / n = 0.74

a)

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.13

Ha: p < 0.13

b)

Test statistics

z = ($\hat p$ - $p_{0}$ ) / $\sqrt{}$ $p_{0}$*(1-$p_{0}$) / n

= ( 0.74 - 0.13) / $\sqrt{}$ (0.13*0.87) / 100

= 18.14

c)

P-value =

= P(Z <z )

= P(Z < 18.14)

= 1

The p-value is p = 1.0, and since p = 1.0 > 0.05, it is concluded that the null hypothesis is fail to rejected.

d)

Do not reject the null hypothesis.