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 two English courses with a standard deviation of 0.7. The females took an average of three English courses with a standard deviation of 0.9. Are the means statistically the same? (Use ox = 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.) Part (a) Part (b) Part (c) Part (d) State the distribution to use for the test. (Enter your answer in the form z or toy where of is the degrees of freedom. Round your answer to two decimal places.) Part (e) 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.) --Select-- = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If Ho is false, then there is a chance equal to the p-value that the difference in the sample mean number of English courses taken by males and females is at least 1. If Ho is true, then there is a chance equal to the p-value that the difference in the sample mean number of English courses taken by males and females is at least 1. If Ho is false, then there is a chance equal to the p-value that the difference in the sample mean number of English courses taken by males and females is at most 1. If He is true, then there is a chance equal to the p-value that the difference in the sample mean number of English courses taken by males and females is at most 1. Part (9) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. 1/2(p-value) 1/2(p-value p-value - XM - XF XM - XF 1/2(p-value) 1/2(p-value P-value XM - XF XM - XF O Part (h) 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.) a = (ii) Decision: O reject the null hypothesis O do not reject the null hypothesis (iii) Reason for decision: O Since p-value > or, we reject the null hypothesis. Since p-value >