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In: Statistics and Probability

Do men score lower on average compared to women on their statistics ? scores of twelve...

Do men score lower on average compared to women on their statistics ? scores of twelve randomly selected male statistics students and twelve randomly selected female statistics students are shown below.

Male:  71 93 55 93 81 71 90 84 65 64 75 88

Female:  83 99 87 68 64 97 75 73 68 70 99 97

Assume both follow a Normal distribution. What can be concluded at the the αα = 0.01 level of significance level of significance?

For this study, we should use Select an answer t-test for the difference between two dependent population means t-test for the difference between two independent population means z-test for the difference between two population proportions z-test for a population proportion t-test for a population mean

  1. The null and alternative hypotheses would be:   
  2.   

H0:H0:  Select an answer μ1 p1  Select an answer > ≠ < =  Select an answer p2 μ2  (please enter a decimal)   

H1:H1:  Select an answer μ1 p1  Select an answer ≠ > = <  Select an answer p2 μ2  (Please enter a decimal)

  1. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
  2. The p-value =  (Please show your answer to 4 decimal places.)
  3. The p-value is ? > ≤  αα
  4. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean statistics score for men is less than the population mean statistics score for women.
    • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean statistics score for men is less than the population mean statistics score for women.
    • The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean statistics score for men is equal to the population mean statistics score for women.
    • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean score for the twelve men that were observed is less than the mean score for the twelve women that were observed.

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