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) p-value 1/2(p-value) XM - XF p-value XM-XF 1/2(p-value) 1/2(p-value XM-XF XM-XF 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.) απ (ii) Decision: Oreject the null hypothesis O do not reject the null hypothesis (iii) Reason for decision: Since p-value a, we do not reject the null hypothesis. O Since p-value>a, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to show that the mean number of English courses that males and females take is different. There is not sufficient evidence to show that the mean number of English courses that males and females take is different. Part (i) Explain how you determined which distribution to use. ○ The standard normal distribution will be used because the samples are independent and the population standard deviation is known. ○ The t-distribution will be used because the samples are dependent. The t-distribution will be used because the samples are independent and the population standard deviation is not known. The standard normal distribution will be used because the samples involve the difference in proportions. 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 α = 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) State the null hypothesis. ○ Ho μM² HF ○ Ho: μM = HF ○ Ho: μM HF ○ Ho: HMSμF ○ HoμM HF ○ Ha: HM SHF Part (c) In words, state what your random variable XM-XF represents. OXM-X represents the mean number of English courses taken by males and females. OXM-XF represents the difference in number of English courses taken by males and females. OXM-XF represents the mean difference in the number of English courses taken by males and females. OXM-XF represents the difference in the mean number of English courses taken by males and females. Part (d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df 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 most 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 most 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 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.

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) p-value 1/2(p-value) XM - XF p-value XM-XF 1/2(p-value) 1/2(p-value XM-XF XM-XF 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.) απ (ii) Decision: Oreject the null hypothesis O do not reject the null hypothesis (iii) Reason for decision: Since p-value a, we do not reject the null hypothesis. O Since p-value>a, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to show that the mean number of English courses that males and females take is different. There is not sufficient evidence to show that the mean number of English courses that males and females take is different. Part (i) Explain how you determined which distribution to use. ○ The standard normal distribution will be used because the samples are independent and the population standard deviation is known. ○ The t-distribution will be used because the samples are dependent. The t-distribution will be used because the samples are independent and the population standard deviation is not known. The standard normal distribution will be used because the samples involve the difference in proportions. 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 α = 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) State the null hypothesis. ○ Ho μM² HF ○ Ho: μM = HF ○ Ho: μM HF ○ Ho: HMSμF ○ HoμM HF ○ Ha: HM SHF Part (c) In words, state what your random variable XM-XF represents. OXM-X represents the mean number of English courses taken by males and females. OXM-XF represents the difference in number of English courses taken by males and females. OXM-XF represents the mean difference in the number of English courses taken by males and females. OXM-XF represents the difference in the mean number of English courses taken by males and females. Part (d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df 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 most 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 most 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 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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