Question

The mean number of English courses taken in a two–year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 25 males and 13 females. The males took an average of 4 English courses with a standard deviation of 0.8. The females took an average of 2.5 English courses with a standard deviation of 1.0.

Set up a hypothesis test to determine whether this difference is statistically significant at the level ?=0.05.

a. State the null and alternative hypothesis.

Select your answer from one of the following options.

• a.

  ?0:??−??≤0??:??−??>0

• b.

  ?0:??−??≥0??:??−??<0

• c.

  ?0:??−??≠0??:??−??=0

• d.

  ?0:??−??=0??:??−??≠0

  b. Calculate the standardized test statistic ?=(?⎯⎯⎯?−?⎯⎯⎯?)−(??−??)?2???+?2???‾‾‾‾‾‾‾‾√

  Round your answer to 2 decimal places.

  c. Calculate the p-value for the hypothesis test using a t-distribution with 36 degrees of freedom. Round your answer to 4 decimal places.

  d. Draw a conclusion and interpret your result.

  Select your answer from one of the following options.
  • a.

    Fail to reject the null hypothesis. There is evidence of a statistically significant difference in the average number of English courses for males and females.

  • b.

    Fail to reject the null hypothesis. There is not enough evidence to conclude that the average number of English courses is different for males and females.

  • c.

    Reject the null hypothesis. There is evidence of a statistically significant difference in the average number of English courses for males and females.

  • d.

    Reject the null hypothesis. There is not enough evidence to conclude that the average number of English courses is different for males and females.

Answer 1

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