Note: Unless a question indicates otherwise, if you are asked to perform a hypot

Question

Note: Unless a question indicates otherwise, if you are asked to perform a hypothesis test you may either find the relevant statistics and carry out the test “by hand” or use a computer to perform the test directly. If you do the latter, please note what formula(s) and statistical distributions the computer has used and what values were substituted into the formula(s) in performing the test. Also, don’t forget to interpret the p-value from your test to draw a conclusion about the assumption being tested.

Question; It has been suggested that students are under more time pressure than business people and therefore that Student users could be expected to walk across the bridge more quickly than Business users. The average time taken by the 260 Student users in this sample to cover the designated 10 metre section was 6.571 seconds, with a (sample) standard deviation of 0.740 seconds, while the average time for the 79 Business users was 6.713 seconds, with a standard deviation of 1.427 seconds.
Assuming equal standard deviations for these two user groups, test the assumption that the mean time taken by Student users of the Goodwill Bridge is less than the mean time taken by Business users. Use a significance level of = 0.1 to draw your conclusion in this case.

Explanation / Answer

Null HYpothesis : H0 : There is no difference in average time taken by business users and school students.

µbusiness = µstudents

Alternative Hypothesis : Ha : Students take less average time than business users to pass the bridge.

µbusiness < µstudents

Statistics

Here equal standard deviations for these two user groups.

so we will perform t - test for equal variances.

pooled standard deviation sp = sqrt [ (n1 -1)s1 2 + (n2 -1)s2 2/(n1 + n2 -2)]

sp = sqrt [ 259 * 0.7402 + 78 * 1.4272 / (259+ 78)] = 0.9445

so Test Statistic

t = (xbusienss - xstudents)/ sp sqrt [1/n1 + 1/n2 ] = (6.713 - 6.571)/ 0.9445 * sqrt (1/260 + 1/79)

t = 0.142 / 0.1213 = 1.17

For alpha = 0.1 and dF = 337

tcritical = 1.284

so here t < tcritical so we cannot reject the null hypothesis and can conclude that there is no significant difference in the mean time taken by Student users to cross Goodwill Bridge than the mean time taken by Business users.

Students Businessmen Average time 6.571 6.713 Standard Deviation 0.740 1.427 Sample size 260 79

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