BA275 Assignment 5

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. a. State the null hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. = 24.57 2. /= 24.57 3. > 24.57 Choose correct answer from above choice State the alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. /= 24.57 2. = 24.57 3. > 24.57 Choose correct answer from above choice

1 1

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience a population standard deviation of = $1,600 may be assumed. What is the p-value (to 4 decimals)?

=0.0340 Z= (xbar-u)/(sigma/sqrt n)

Consider the following hypothesis test: H0: ≤ 25 Ha: > 25 A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. c. At = .01, what is your conclusion?

>0.01 Fail to reject

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention. H0: Ha:

>= 1056 < 1056

Consider the following hypothesis test: H0: ≤ 25 Ha: > 25 A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. d. What is the rejection rule using the critical value? Reject H0 if z is ___________ What is your conclusion?

>= 2.33 C.V. is Zcrit==> Z0.01= 2.33 1.48<2.33 so we fail to reject

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries c. With = .05 as the level of significance, what is your conclusion?

As P > 0.05, we FAIL TO REJECT HO. There is no significant evidence that the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries.

Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. b. What is the p-value (to 4 decimals)?

B) Also, the p value is p = 0.045126949 [answer]

Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. c. Using = .05, can it be concluded that the population mean is not equal to 15?

C) As P < 0.05, YES, we can conclude that the populaiton mean is not equal to 15. [ANSWER, YES] **********************

Consider the following hypothesis test: H0: ≤ 25 Ha: > 25 A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. b. What is the p-value (to 4 decimals)?

Test statistic 1.48 P(Z>1.48) P-value= 0.0694

Consider the following hypothesis test: H0: ≤ 25 Ha: > 25 A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. a. Compute the value of the test statistic (to 2 decimals).

Test statistic z= (xbar - u)/ (sigma/sqrt n) =1.48

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). d. Using = .05, what is the critical value for the test statistic?

Ztable0.05=1.645 on the left so it is -1.645

Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. a. Compute the value of the test statistic (to 2 decimals).

a) Formulating the null and alternative hypotheses, Ho: u = 15 Ha: u =/ 15 As we can see, this is a two tailed test. Getting the test statistic, as X = sample mean = 14.15 uo = hypothesized mean = 15 n = sample size = 50 s = standard deviation = 3 Thus, z = (X - uo) * sqrt(n) / s = -2.003469213 [ANSWER]

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries b. Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value. Round your answer to four decimal places.

b. Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value. Round your answer to four decimal places. Formulating the null and alternative hypotheses, Ho: u = 24.57 Ha: u =/ 24.57 As we can see, this is a two tailed test. Getting the test statistic, as X = sample mean = 23.89 uo = hypothesized mean = 24.57 n = sample size = 30 s = standard deviation = 2.4 Thus, z = (X - uo) * sqrt(n) / s = -1.55188058 Also, the p value is p = 0.120690801 [ANSWER]

Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. d. Using = .05, what are the critical values for the test statistic? (+ or -)

d) At 0.05 level, the critical values are z = +/- 1.96 [ANSWER]

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries d. Repeat the preceding hypothesis test using the critical value approach. Round your answer to two decimal places. Enter negative values as negative numbers.

d. The critical value(s) is(are): Thus, getting the critical z, as alpha = 0.05 , alpha/2 = 0.025 zcrit = +/- 1.959963985 Thus, d. +/- 1.96 [ANSWER]

Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. e. State the rejection rule: Reject H0 if z is the lower critical value and the upper critical value.

e) Reject Ho if z is LESS THAN the lower critical value and GREATER THAN the upper critical value. *************************

Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3 f. Can it be concluded that the population mean is not equal to 15?

f) YES, becasue zstat < -1.96. [ANSWER]

Carpetland salespersons average $8,000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. b. In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales ____ when in fact it does not.

greater than 8000 Type 1 error implies that the null is correct and we still do not accept it. In this context it would mean that the new plan did not result in higher average sales per salesperson and yet it was implemented by Carpetland.

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). e. State the rejection rule: Reject H0 if z is the critical value.

less than or equal to -1.645

The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills to test the manager's claim. a. Which form of the hypotheses should be used to test the manager's claim?

less than or equal to 600 greater than 600

Carpetland salespersons average $8,000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. c. In this situation, a Type II error would occur if it was concluded that the new compensation plan provides a population mean weekly sales_____when in fact it does not.

less than or equal to 8000 Type 2 error implies that the alternative hypothesis is true but it is not accepted, instead the null is accepted. In this case the new plan did increase sales per averages salesperson but it was not implemented-this causes potential losses to the firm as higher sales could have been realized but they were actually not realized, as the plan was not implemented.

Carpetland salespersons average $8,000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. a. Develop the appropriate null and alternative hypotheses.

less than or equal to 8000 greater than 8000

The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills to test the manager's claim. b. When H0 cannot be rejected, can we conclude that the manager's claim is wrong?

no

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). c. Using = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers?

yes

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). f. Using = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers?

yes

The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills to test the manager's claim. c. When H0 can be rejected, can we conclude that the manager's claim is wrong?

yes