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March 30, 2017

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A psychological test was given to 92 teenage boys and 68 teenage girls. The test was used to assign a score to each teenager, measured on the ‘worry scale’ – 0 (not worried) to 100 (very worried). A summary of the results is given in the table below.

Girls; Sample Size 68
Sample Mean 58.52
Sample Standard Deviation 8.61
Boys; Sample Size 92
Sample Mean 64.28
Sample Standard Deviation 8.96

Q1) Choose the option that gives, to two decimal places, the estimated standard error (ESE) of the difference between the sample means for girls and boys.
A 1.40 B 1.65 C 1.73 D 1.98 E 2.00 F 2.06

Q2) The two-sample z-test is to be used to determine whether there is a difference, at the 5% significance level, between the mean scores for girls and boys. Choose the TWO options that give the value of the test statistic z, to two decimal places, and the conclusion obtained from the test.

A 4.11 B 4.50 C 4.86
D 5.00 E 8.77 F 87.71
G There seems to be a significant difference, at the 5% significance level, between the mean scores for girls and boys.
H There seems to be no significant difference, at the 5% significance level, between the mean scores for girls and boys.

  • Math - ,

    Z = (mean1 - mean2)/standard error (SE) of difference between means

    SEdiff = √(SEmean1^2 + SEmean2^2)

    SEm = SD/√(n-1)

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

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