Question

Question 1: Choose the best option:

I-A search engine optimization (SEO) company would like to know whether the market share in web search is still split as expected between Google, Bing, Yahoo, and all others combined. He sampled 1200 observations for this study. Which test would he use?

a. A χ2\chi^2 test with 1196 df

b. A χ2\chi^2 test with 3 df

c. A test of independence with 1197 df

d. A test of independence with 2 df

e. A χ2\chi^2 test with 1197 df

II- Suppose the competing hypotheses for a test are H0:µ1=µ2H_0 : µ_1 = µ_2 versus Ha:µ1≠µ2H_a : µ1 ≠ µ2. A 95% confidence interval for the mean difference (µ1–µ2)(µ_1 – µ_2) is calculated to be (-6.3, 3.4). At the 5% significance level, the correct conclusion to the hypothesis test is

a. Do not reject H0, the means are not the same

b. Do not reject H0, we can’t prove the means are different

c. We do not have enough information to make any conclusion

d. Reject H0, the means are the same

e. Reject H0, the means are not the same

III-Which of the following tables can be used as a more exact substitute for the empirical rule?

a. Z table

b. F table

c. T table

d. Chi-squared table

e. None of the above

IV-Which of the following is true about Chi-square tests and F tests?

a. Both have test statistics between 0 and infinity

b. Both have numerator degrees of freedom and denominator degrees of freedom

c. Both have test statistics between negative infinity and infinity

d. Both measure the discrepancies between expected and observed frequencies

e. Both have test statistics between 0 and 1

Answer 1

(I) b. A test with 3 df

(Here there are 4 rows Google, Yahoo bing and all others combined. Thus, df = 4-1=3, moreover here we would like to know whether the market share in web search is still split as expected)

(II) The 100(1-)% CI for () is given by (-6.3,3.4) where =0.05

c. We do not have enough information to make any conclusion

(From confidence interval, we cannot make any decision of acceptance or rejection.)

(III)The table can be used as a more exact substitute for the empirical rule is

a. Z table

( the emperical rule, which is 68,95,99.7 rule for normal distribution can be sustituted by the usage of Z table )

(IV) a. Both have test statistics between 0 and infinity

( Both chi square and F test statistic take non negative values)