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 29 males and 16 females. The males took an average of four English courses with a standard deviation of 0.7. The females took an average of five English courses with a standard deviation of 1.2. Are the means statistically the same? (Use ? = 0.05)
NOTE: If you are using a Student's
t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
1.State the distribution to use for the test. (Enter your answer in the form
z
or
t
df
where
df
is the degrees of freedom. Round your answer to two decimal places.)
2. What is the test statistic? (If using the
z
distribution round your answer to two decimal places, and if using the
t
distribution round your answer to three decimal places.)
T or Z = ?
3. What is the
p-value? (Round your answer to four decimal places.)
4.Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =