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MAT240S MAT 2021 GROUP ASSIGNMENT INFERENTIAL DATA ANALYSIS \ Group : PPgirl A. Estimation of Parameters (mean and proportion) (i) Population mean of spo rts time (hours) n = 151, x = 1.687, s = 2.739 95% CI, df = 1 50, critical value = +-1.660 Pop ulation mean = 0.440 Population mean of sleep time (hours) n = 151, x = 7.811, s = 3.798 95% CI, df = 150, critical value = + -1.660 Population mean = 0.611 (ii) Popul ation p roportion of gender n = 151, p = 0.424, q = 0.576 95% CI, critical value = 0.5199 Population proportion = 0.424 Popul ation p roportion of on time n = 151, p = 0.921, q = 0. 079 95% CI, critical value = 0.5199 Population proportion = 0.921 B. Hypothesi s testing of population m ean and proportion (i) Population mean of age Claim : Mea n> 15 (Right Tail) Ho : Mean<= 15 H1: Mean>20 c.v . = 1.976 Reject Ho if z is > 1.976 Z = (20 -15 )/(1.993/ 12.188) = 30. 577 Ho is not rejected since z -value is not less than or equal to rejection region. There fore , we can infer that the claim is true. Population mean of working hour Claim : Mea n<10 (Left Tail) Ho : Mean >= 10 H1: Mean <10 c.v . = 1.976 Reject Ho if z is <1.976 Z = (7-10 )/(11.416 /12.188) = -3.203 Ho is not rejected since z -value is not more than or equal to rejection region. There fore , we can infer that the claim is true . Population mean of electroni c gadgets time Claim : Mea n = 10 (Tw o Tail) Ho : Mean = 10 H1: Mean /= 10 c.v . = 1.976 Reject Ho if z is equal to 1.976 Z = (10 -8)/(5.5 5/12.188) = 4.392 Ho is rejected since z -value is not equal to rejection region. There fore , we can not infer that the claim is true. (ii) Popul ation proportion of major Claim = Major in Bu siness Ho : M = Business H1: M /= Business c.v . = 1.976 Reject Ho if z is equal to 1.976 Z = (65 -0.430)/((0.43*0.57)/151) = 10.75 Ho is rejected since z -value is not equal to rejection region. There fore , we can not infer that the claim is true. C. Hypothesis testing of two population means / two population proportions (i) Population Mean of 2 Sample Claim = Local > International Ho : L = I H1: L > I c.v . = 2.060 Reject Ho if z is equal to 2.060 Z = ((10 -8)/(7.998 /12.188) ) = 3.060 Ho is rejected since z -value is not equal to rejection region. There fore , we can not infer that the claim is true. (iii) Popul ation proportion of Procrastinate Claim = Local Procrastinate < International Pro crastinate Ho : LP = IP H1: LP < IP c.v . = 1.976 Reject Ho if z is equal to 1.976 Z = ((93 -16 )/((0.853*0.147) /12.188) )) = 2.990 Ho is rejected since z -value is not equal to rejection region. There fore , we can not infer that the claim is true. D. Hypothesis testing of more than 2 population mea ns. Hypothesis testing among mean of sleep hours among student in difference education level Claim = There is difference in the mean sleep hours among student in difference educational le vel. Ho : There is difference H1: There is no difference c.v . = 2.0 17 Reject Ho if z is equal to 2.017 Z = ((10 -8)/(7.998 /12.18 )) = 4.788 Ho is rejected since z -value is not equal to rejection region. There fore , we can not infer that the claim is true. E. Hypothesis testing of relationship between categorical variables. Observed Counts Yes No Total Chinese 36 81 117 Malay 5 7 12 Indian 9 5 14 Others 3 5 8 Total 53 98 151 Expected Counts Yes No Total Chinese 41.06623 75.93377 117 Malay 4.211921 7.788079 12 Indian 4.913907 9.086093 14 Others 2.807947 5.192053 8 Total 53 98 151 x2 Yes No Total Chinese 0.62501 0.33801 0.96302 Malay 0.14746 0.07975 0.2272 Indian 3.39773 1.83755 5.23529 Others 0.01314 0.0071 0.02024 Total 4.18333 2.26241 6.44575 Degree of Freedom = 3 P-Value = 0.092