Question

A random sample of 100 students at a high school was asked whether they would ask their father or mother for help with a financial problem. A second sample of 100 different students was asked the same question regarding a dating problem. If 43 students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for help, test the hypothesis of no difference in the proportions. Use α = 0.02.
- Identify the null hypothesis and alternative hypothesis
- Identify the test statistic
- Identify the critical value(s)
- Identify the final conclusion that addresses the original claim: a) Fail to reject Ho, there is sufficient evident to warrant rejection of the claim that no difference in the proportions. b) Reject Ho, there is sufficient evident to warrant rejection of the claim that no difference in the proportions. c) Fail to reject Ho, there is not sufficient evident to warrant rejection of the claim that no difference in the proportions. d) Fail to reject Ho, there is not sufficient evident to support the claim that no difference in the proportions.

Answer 1

Solutions. The provided fofoncomition is as followers for sample sample size = 100 number of fawrable cases Sample-propostion pı = x1 = 43 -0.43 X= 43 nu 100 For sample 21 somple size n2 = 100 number of favorable cases X2 = 47 sample proportion p2= 12 47 0.47 na 100 Also the provided significance level is x=0.02 The role of the pooled proportion is computed - ast 4.3+47 0.45 X14X2 nitoa 100 + 10o • Identify the aull bypothesis and alternatie hypothesis. The following null and alternative hypotheses need to be tested. Ho pl = P2 Hai pl #p2 Comresponds to This a two tailed test for which z-test for two population proportions needs to be conducted.

I dentify the test statistic. The 3-statistic is computed as follows; Pi - p2 PCI-P2 ( 1 ) n2 0.43 -0.47 0-45(1-0.45) 100 ( 16 ) 100 z = -0.569 Identify the critical value (s) Based on the information provided, the significance level. is R30.02, and the citical value for a two tailed test is z 2.33 The rejection region for this two tailed test iĝ; z<- 2:33 232,33] zo - 2.33 or R=42: ZE-$96 Here Z=-0.56g Ze=-2.33 and 2 = o.sog< z = 2.33 Therefore it is concluded that the null hypothesis is not rejected:

• Identify the facil.conclusion that addresses the anginal class i 'It is concluded that the null hypothesis. Ho is not rejected. Therefore option c) fail to reject Ho, there is not sufficient evident to warrant rejection of the claim that no difference in the proportions is the comect option: