Randomly selected students were given five seconds to estimate the value of a product of numbers with the results shown below.
Estimates from students given $1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8$: $$50, \ 1252, \ 25, \ 856, \ 800, \ 10000, \ 800, \ 2000, \ 500, \ 200$$ Estimates from students given $8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$: $$377, \ 49000, \ 1876, \ 200, \ 1500, \ 225, \ 1500, \ 400, \ 5000, \ 3600$$ Use a $0.05$ significance level to test the following claims:
1. $\ $ Claim: the two populations have equal variances.
The test statistic is
The larger critical value is
The conclusion is
A. There is sufficient evidence to warrant the rejection of the claim that the two populations have equal variances
B. There is not sufficient evidence to warrant the rejection of the claim that the two populations have equal variances
2. $\ $ Claim: the two populations have the same mean. The test statistic is
The positive critical value is
The negative critical value is
The conclusion is
A. There is not sufficient evidence to warrant the rejection of the claim that the two populations have the same mean
B. There is sufficient evidence to warrant the rejection of the claim that the two populations have the same mean