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 0.9. The females took an average of five English courses with a standard deviation of 1.1. Are the means statistically the same? (Use a = 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.) O Part (a) O Part (b) O Part (c) O Part (d) O Part (e) O Part () What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. O 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. O If H, 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. O 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. O 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 most 1. O Part (g) 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- Xp XM - Xp 1/2(p-value) 1/2(p-value p-value XM - Xp XM - Xp
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![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 0.9. The females took an average of five English courses with a standard deviation of 1.1. Are the means statistically the same? (Use a = 0.05)
NOTE: If you are using
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.)
O Part (a)
O Part (b)
O Part (c)
O Part (d)
O Part (e)
O Part (f)
What is the p-value? (Round your answer
four decimal places.)
Explain what the p-value means for this problem.
O If H, 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.
O If H, 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.
O 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.
O 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 most 1.
O Part (g)
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 - Xp
1/2(p-value)
1/2(p-value
p-value
XM - Xp
XM - Xp](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45a83661-9fd2-4d7a-ac7c-cc7e2b77af54%2F3af81f03-a2f8-4b98-aee9-b15a4ee9504b%2F6sunbb1_processed.jpeg&w=3840&q=75)
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Given:
The mean number of English courses taken in a two-year time period by male and female college students is believed to be same; that is;
where,
be the mean number of English courses taken in a two-year time period by male.
be the mean number of English courses taken in a two-year time period by female.
be the number of males; that is; = 29.
be the number of females; that is; = 16.
be the sample mean of English courses taken in a two-year time period by male; that is; =4.
be the sample mean of English courses taken in a two-year time period by female; that is; =5.
be the sample standard deviation of male; that is; =0.9.
be the sample standard deviation of females; that is; =1.1.
The hypothesis that can be formed are:
Null hypothesis (H0):
Alternate Hypothesis (H1):
The test here is two tailed t test.
The value of test statistics can be calculated as:
where, the value of is calculated as:
Hence, the value of test statistics is obtained as -3.295.
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