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Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. p-value 1/2(p-value) p-value Xm - X 1/2(p-value Xm - X 1/2(p-value) 1/2(p-value) Âm - Xe Xm - Xe 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.) α= (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. ○ Since p-value>a, we reject the null hypothesis. ○ Since p-value

Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. p-value 1/2(p-value) p-value Xm - X 1/2(p-value Xm - X 1/2(p-value) 1/2(p-value) Âm - Xe Xm - Xe 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.) α= (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. ○ Since p-value>a, we reject the null hypothesis. ○ Since p-value

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. p-value 1/2(p-value) p-value Xm - X 1/2(p-value Xm - X 1/2(p-value) 1/2(p-value) Âm - Xe Xm - Xe 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.) α= (ii) Decision: Oreject the null hypothesis O do not reject the null hypothesis (iii) Reason for decision: Since p-value <a, we reject the null hypothesis. O Since p-value>a, we do not reject the null hypothesis. ○ Since p-value>a, we reject the null hypothesis. ○ Since p-value <a, we do not reject the null hypothesis. (iv) Conclusion: ○ There is sufficient evidence to show that the mean entry level mechanical engineering salary is lower than the mean entry level electrical engineering salary. ○ There is not sufficient evidence to show that the mean entry level mechanical engineering salary is lower than the mean entry level electrical engineering salary. Part (i) Explain how you determined which distribution to use. The standard normal distribution will be used because the samples involve the difference in proportions. ○ 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 independent and the population standard deviation is not known. The t-distribution will be used because the samples are dependent.
Transcribed Image Text:Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. p-value 1/2(p-value) p-value Xm - X 1/2(p-value Xm - X 1/2(p-value) 1/2(p-value) Âm - Xe Xm - Xe 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.) α= (ii) Decision: Oreject the null hypothesis O do not reject the null hypothesis (iii) Reason for decision: Since p-value <a, we reject the null hypothesis. O Since p-value>a, we do not reject the null hypothesis. ○ Since p-value>a, we reject the null hypothesis. ○ Since p-value <a, we do not reject the null hypothesis. (iv) Conclusion: ○ There is sufficient evidence to show that the mean entry level mechanical engineering salary is lower than the mean entry level electrical engineering salary. ○ There is not sufficient evidence to show that the mean entry level mechanical engineering salary is lower than the mean entry level electrical engineering salary. Part (i) Explain how you determined which distribution to use. The standard normal distribution will be used because the samples involve the difference in proportions. ○ 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 independent and the population standard deviation is not known. The t-distribution will be used because the samples are dependent.
Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 42 entry level mechanical engineers and 56 entry level electrical engineers. Their mean salaries were $46,200 and $46,700, respectively. Their standard deviations were $3430 and $4250, respectively. Conduct a hypothesis test at the 5% level to determine f you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary. Let the subscript m = mechanical and e = electrical. 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: Hm < не o Ho khm the Part (b) State the alternative hypothesis. ○ Hg: μm #He Ha: μm He Ha: μm = He Ha μm <He Part (c) In words, state what your random variable Xm - Xe represents. Oxm-Xe represents the mean difference in the starting salaries of entry-level mechanical engineers and electrical engineers. Oxm-X represents the difference in the mean starting salaries of entry-level mechanical engineers and electrical engineers. Oxm-X represents the difference in starting salaries of entry-level mechanical engineers and electrical engineers. Oxm-X represents the mean starting salary of entry-level mechanical engineers and electrical engineers. 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 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 true, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is $500 more than the sample mean salary of electrical engineers. If Ho is false, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is $500 more than the sample mean salary of electrical engineers. If Ho is true, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is at least $500 less than the sample mean salary of electrical engineers. If Ho is false, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is at least $500 less than the sample mean salary of electrical engineers.
Transcribed Image Text:Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 42 entry level mechanical engineers and 56 entry level electrical engineers. Their mean salaries were $46,200 and $46,700, respectively. Their standard deviations were $3430 and $4250, respectively. Conduct a hypothesis test at the 5% level to determine f you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary. Let the subscript m = mechanical and e = electrical. 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: Hm < не o Ho khm the Part (b) State the alternative hypothesis. ○ Hg: μm #He Ha: μm He Ha: μm = He Ha μm <He Part (c) In words, state what your random variable Xm - Xe represents. Oxm-Xe represents the mean difference in the starting salaries of entry-level mechanical engineers and electrical engineers. Oxm-X represents the difference in the mean starting salaries of entry-level mechanical engineers and electrical engineers. Oxm-X represents the difference in starting salaries of entry-level mechanical engineers and electrical engineers. Oxm-X represents the mean starting salary of entry-level mechanical engineers and electrical engineers. 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 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 true, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is $500 more than the sample mean salary of electrical engineers. If Ho is false, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is $500 more than the sample mean salary of electrical engineers. If Ho is true, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is at least $500 less than the sample mean salary of electrical engineers. If Ho is false, then there is a chance equal to the p-value that the sample mean salary of mechanical engineers is at least $500 less than the sample mean salary of electrical engineers.
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