Question

1) A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 323 people over the age of​ 55, 66 dream in black and​ white, and among 281people under the age of​ 25,15 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts​ (a) through​ (c) below.

2) A simple random sample of​ front-seat occupants involved in car crashes is obtained. Among 2728 occupants not wearing seat​ belts, 31 were killed. Among 7791occupants wearing seat​ belts, 17 were killed. Use a 0.01 significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts​ (a) through​ (c) below.

3)Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1408 referee​ calls, with the result that 430 of the calls were overturned. Women challenged 767 referee​ calls, and 228 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below.

Answer 1

1)

Here we have 66, n 323,P1 0.2043 x,-15, n-281p, =x2/n,-0.0534 Hypotheses are α =0.05 Level of significance Test is right tailed The pooled proportion is -(66+15)/(323+281)-0.1341 The standard error is: SE p(1 pl-p)-0.0278 Test Statistics: (P.-pi)-(2-2)=5.43 - SE Critical value: CV 1.64 Rejection Region: If 리 > 1.64, Reject H0 Decision: Since test statistics lies in rejection region so we reject the null hypothesis P-value -0 Decision: Since p-value is less than level of significance so we reject the null hypothesis Excel function for critical value: Excel function for p-value: =NORMSINV(1-0.05) (1-NORMSDIST(5.43))