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2. Point Estimation, Confidence Interval and Hypothesis Testing A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean of all ABC broker clients is $18.75. A sample of 100 clients of XYZ is taken, the mean of the sample is $18 and the standard deviation is $6. a. Construct a 90% confidence interval for the mean brokerage fee of XYZ. b. Assume that the standard deviation of all XYZ's brokerage fee is $6 (unknown. Please formulate a Hypothesis Testing to decide whether you will switch to the new broker. C. Assume that the standard deviation of all XYZ's brokerage fee is $6. Please use the C.I. Estimation method to construct a hypothesis test for the hypothesis in (b). d. Assume that the standard deviation of all XYZ's brokerage fee is unknown and a new sample of 25 clients of ABC is taken. The sample mean is $17.8 and the sample standard deviation is $3. Based on the new sample, will you change your mind (whether switch to a broker with lower fee)? e. In the preliminary sample in (d) of 25 clients, 5 clients decided not to come to his business next time. The stockbroker would like to estimate the population proportion of clients who would not come to his business next time with a 99% confidence interval within ±0.12 (margin of error). How much larger a sample needs to be taken? (What is the required sample size?)

2. Point Estimation, Confidence Interval and Hypothesis Testing A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean of all ABC broker clients is $18.75. A sample of 100 clients of XYZ is taken, the mean of the sample is $18 and the standard deviation is $6. a. Construct a 90% confidence interval for the mean brokerage fee of XYZ. b. Assume that the standard deviation of all XYZ's brokerage fee is $6 (unknown. Please formulate a Hypothesis Testing to decide whether you will switch to the new broker. C. Assume that the standard deviation of all XYZ's brokerage fee is $6. Please use the C.I. Estimation method to construct a hypothesis test for the hypothesis in (b). d. Assume that the standard deviation of all XYZ's brokerage fee is unknown and a new sample of 25 clients of ABC is taken. The sample mean is $17.8 and the sample standard deviation is $3. Based on the new sample, will you change your mind (whether switch to a broker with lower fee)? e. In the preliminary sample in (d) of 25 clients, 5 clients decided not to come to his business next time. The stockbroker would like to estimate the population proportion of clients who would not come to his business next time with a 99% confidence interval within ±0.12 (margin of error). How much larger a sample needs to be taken? (What is the required sample size?)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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2. Point Estimation, Confidence Interval and Hypothesis Testing A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean of all ABC broker clients is $18.75. A sample of 100 clients of XYZ is taken, the mean of the sample is $18 and the standard deviation is $6. a. Construct a 90% confidence interval for the mean brokerage fee of XYZ. b. Assume that the standard deviation of all XYZ's brokerage fee is $6 (unknown. Please formulate a Hypothesis Testing to decide whether you will switch to the new broker. C. Assume that the standard deviation of all XYZ's brokerage fee is $6. Please use the C.I. Estimation method to construct a hypothesis test for the hypothesis in (b). d. Assume that the standard deviation of all XYZ's brokerage fee is unknown and a new sample of 25 clients of ABC is taken. The sample mean is $17.8 and the sample standard deviation is $3. Based on the new sample, will you change your mind (whether switch to a broker with lower fee)? e. In the preliminary sample in (d) of 25 clients, 5 clients decided not to come to his business next time. The stockbroker would like to estimate the population proportion of clients who would not come to his business next time with a 99% confidence interval within ±0.12 (margin of error). How much larger a sample needs to be taken? (What is the required sample size?)
Transcribed Image Text:2. Point Estimation, Confidence Interval and Hypothesis Testing A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean of all ABC broker clients is $18.75. A sample of 100 clients of XYZ is taken, the mean of the sample is $18 and the standard deviation is $6. a. Construct a 90% confidence interval for the mean brokerage fee of XYZ. b. Assume that the standard deviation of all XYZ's brokerage fee is $6 (unknown. Please formulate a Hypothesis Testing to decide whether you will switch to the new broker. C. Assume that the standard deviation of all XYZ's brokerage fee is $6. Please use the C.I. Estimation method to construct a hypothesis test for the hypothesis in (b). d. Assume that the standard deviation of all XYZ's brokerage fee is unknown and a new sample of 25 clients of ABC is taken. The sample mean is $17.8 and the sample standard deviation is $3. Based on the new sample, will you change your mind (whether switch to a broker with lower fee)? e. In the preliminary sample in (d) of 25 clients, 5 clients decided not to come to his business next time. The stockbroker would like to estimate the population proportion of clients who would not come to his business next time with a 99% confidence interval within ±0.12 (margin of error). How much larger a sample needs to be taken? (What is the required sample size?)
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