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 from29 malesand16 females.The males took an average offourEnglish courses with a standard deviation of0.9. The females took an average offiveEnglish courses with a standard deviation of1.2. Are the means statistically the same? (Use?= 0.05)

NOTE: If you are using a Student'st-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.)

Be Careful with the Rounding and try to use all decimals points when needed

• Part (a) Multiple Choice
• State the null hypothesis.

a) H₀:?_M?_F

b) H₀:?_M?_F

c) H₀:?_M>?_F

d) H₀:?_M=?_F

e) H₀:?_MF

• Part (b) Multiple Choice
• State the alternative hypothesis.

a) H_a:?_MF

b) H_a:?_M?_F

c) H_a:?_M>?_F

d) H_a:?_M?_F

e) H_a:?_M=?_F

• Part (c) Multiple Choice
• In words, state what your random variableX_MX_Frepresents.

a) X_MX_Frepresents the difference in the mean number of English courses taken by males and females.

b) X_MX_Frepresents the difference in number of English courses taken by males and females.

c) X_MX_Frepresents the mean number of English courses taken by males and females.

d) X_MX_Frepresents the mean difference in the number of English courses taken by males and females.

• Part (d)
• State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom. Round your answer to two decimal places.)
• ______________
• Part (e)
• What is the test statistic? (If using thezdistribution round your answer to two decimal places, and if using thetdistribution round your answer to three decimal places.)
• (t orz)=_________
• Part (f)
• What is thep-value? (Round your answer to four decimal places.)

P= __________

• Explain what thep-value means for this problem. Mulitple Choice

a) IfH₀is false, then there is a chance equal to thep-value that the difference in the sample mean number of English courses taken by males and females is at most 1.

b) IfH₀is true, then there is a chance equal to thep-value that the difference in the sample mean number of English courses taken by males and females is at most 1.

c) IfH₀is true, then there is a chance equal to thep-value that the difference in the sample mean number of English courses taken by males and females is at least 1.

d) IfH₀is false, then there is a chance equal to thep-value that the difference in the sample mean number of English courses taken by males and females is at least 1.

• Part (g)
• Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to thep-value.
• 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.)
• ?=_______
• (ii) Decision:

a) reject the null hypothesis

b) do not reject the null hypothesis

• (iii) Reason for decision:

a) Sincep-value >?, we do not reject the null hypothesis.

b) Sincep-value

c) Sincep-value >?, we reject the null hypothesis.

d) Sincep-value

• (iv) Conclusion:

a) There is sufficient evidence to show that the mean number of English courses that males and females take is different.

b) There is not sufficient evidence to show that the mean number of English courses that males and females take is different.

• Part (i) Multiple Choice
• Explain how you determined which distribution to use.

a) Thet-distribution will be used because the samples are dependent.

b) Thet-distribution will be used because the samples are independent and the population standard deviation is not known.

c) The standard normal distribution will be used because the samples are independent and the population standard deviation is known.

d) The standard normal distribution will be used because the samples involve the difference in proportions.