Question

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 1×2×3×4×5×6×7×81×2×3×4×5×6×7×8:

200, 1500, 1000, 10000, 1560, 856, 200, 2040, 200, 45000200, 1500, 1000, 10000, 1560, 856, 200, 2040, 200, 45000

Estimates from students given 8×7×6×5×4×3×2×18×7×6×5×4×3×2×1:

550, 450, 500, 3500, 2000, 350, 400, 49000, 25000, 40320550, 450, 500, 3500, 2000, 350, 400, 49000, 25000, 40320

Use a 0.050.05 significance level to test the claim that the two populations have the same mean.

(a) The test statistic is ( ).

(b) The conclusion is

A. There is sufficient evidence to warrant the rejection of the claim that the two populations have the same mean
B. There is not sufficient evidence to warrant the rejection of the claim that the two populations have the same mean

Answer 1

Suppose, random variables X and Y denote product obtained in first and second approaches respectively.

We are given with two sets of sample values whose population variance (or standard deviation) is unknown. So we have to perform two sample t-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Degrees of freedom

So, corresponding    [Using R-code '2*(1-pt(0.07542157,36))']

Level of significance

We reject our null hypothesis if .

Here, we observe that .

So, we can not reject our null hypothesis.

Hence,

• (a) The test statistic is 0.07542157.
• (b) The conclusion is B. There is not sufficient evidence to warrant the rejection of the claim that the two populations have the same mean.