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QUESTION 6 The do-it-yourself (DIY) consumer movement has had a profound impa A recent study conducted by the centre for consumer research examined various trails of p ct on the retailing business. ersons ssified as do-it-yourselves and non-do-it-yourselves. One factor considered age. Because younge do-it-yourselves to be younger. The age (in years) of the people in the two groups from the study are summarised as follows: r people are generally healthier but less efficient, it is reasonable to expect Sample mean 41.8 Standard deviation 15.9 Sample size 29 DIY consumers | Non-DIY consumers 47.4 16.2 34 Does the data support the hypothesis that do-it-yourselves are younger, on average than non- do-it-yourselves? Assuming the two population variances are unequal Which one of the following statements is incorrect? 1. Ho : The population mean do-it-yourselves is greater or equal to the population non-do-it- yourselves (or μ D (ND). 2. H The population mean do-it-yourselves is less than population mean non-do-it-yourselves 3. The critical value at 10% level of significance is t(61;0.10) = 1.296 4. The test statistic t1.3813 5. The statistical conclusion is to reject Ho at 10% level

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(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested This corresponds to a left-tailed test, for which a t-test for two population means with two independent samples, with unknown population standard deviations will be use (2)-Rejection Region Based on the information provided, the significance level is a0.10, and the degrees of freedom are df - 59.774. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal Hence, it is found that the critical value for this left-tailed test is te1.296, for a 0.10 and df 59.774 The rejection region for this left-tailed test is R-t:t<-1.296 3 Since it is assumed that the population variances are unequal, the t-statistic is computed as follows 21 +n2-2 1.8- 47.4 -1.381 -184 1 (29-1)15.92+(34-1)16.2211 29+34-2 Since it is observed that t-1.381tc-1.296, it is then concluded that the null hypothesis is rejected Using the P-value approach: The p-value is p = 0.0862, and since p 0.0862 < 0.10, it is concluded that the null hypothesis is rejected It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ| is less than μ2, at the 0.10 significance level The 90% confidence interval is-12.374くμ1-Mg 1.174

2)nd and 3)rd statements are incorrect

as Ha : mu1 <= mu2
as critical value is -1.296 and not 1.296

Option 2 ) AND 3) are correct

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  • QUESTION 6 The do-it-yourself (DIY) consumer movement has had a profound impact on the retailing business....

    QUESTION 6 The do-it-yourself (DIY) consumer movement has had a profound impact on the retailing business. A recent study conducted by the centre for consumer research examined various trails of persons classified as "do-it-yourselves" and "non-do-it-yourselves". One factor considered was a person's age. Because younger people are generally healthier but less efficient, it is reasonable to expect do-it-yourselves to be younger. The age (in years) of the people in the two groups from the study are summarised as follows: Sample...

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