Compute the mean of the sample means

Question

Solve the following:

Q1: At the downtown office of First National Bank, there are five tellers. Last week, the tellers made the following number of errors each: 2, 3, 5, 3, and 5.

a.How many different samples of 2 tellers are possible?

b.List all possible samples of size 2 and compute the mean of each.

c.Compute the mean of the sample means and compare it to the population mean.

 

Q2: Power+, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35.0 hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power+, Inc. tests samples of 25 batteries.

a.What can you say about the shape of the distribution of the sample mean?

b.What is the standard error of the distribution of the sample mean?

c.What proportion of the samples will have a mean useful life of more than 36 hours?

d.What proportion of the sample will have a mean useful life greater than 34.5 hours?

e.What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours?

Q3: Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000.

a.If we select a random sample of 50 households, what is the standard error of the mean?

b.What is the expected shape of the distribution of the sample mean?

c.What is the likelihood of selecting a sample with a mean of at least $112,000?

d.What is the likelihood of selecting a sample with a mean of more than $100,000?

e.Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000

Q4: A survey of 36 randomly selected "iPhone" owners showed that the purchase price has a mean of $416 with a sample standard deviation of $180.

a.Compute the standard error of the sample mean.

b.Compute the 95% confidence interval for his mpg.

c.How large a sample is needed to estimate the population mean within $10?

Q4: Refer to the Real Estate data, which report information on homes sold in the Goodyear, Arizona, area during the last year.

a.Develop a 95% confidence interval for the mean selling price of the homes.

b.Develop a 95% confidence interval for the mean distance the home is from the center of the city.

c.Develop a 95% confidence interval for the proportion of homes with an attached garage.

d.To report your findings, write a business style memo to Gary Loftus, the president of the Goodyear Chamber of Commerce.

	Price	Bedrooms	Size	Pool	Distance	Twnship	Garage	Baths
	263.1	4	2300	1	17	5	1	2
	182.4	4	2100	0	19	4	0	2
	242.1	3	2300	0	12	3	0	2
	213.6	2	2200	0	16	2	0	2.5
	139.9	2	2100	0	28	1	0	1.5
	245.4	2	2100	1	12	1	1	2
	327.2	6	2500	0	15	3	1	2
	271.8	2	2100	0	9	2	1	2.5
	221.1	3	2300	1	18	1	0	1.5
	266.6	4	2400	0	13	4	1	2
	292.4	4	2100	0	14	3	1	2
	209	2	1700	0	8	4	1	1.5
	270.8	6	2500	0	7	4	1	2
	246.1	4	2100	0	18	3	1	2
	194.4	2	2300	0	11	3	0	2
	281.3	3	2100	0	16	2	1	2
	172.7	4	2200	1	16	3	0	2
	207.5	5	2300	1	21	4	0	2.5
	198.9	3	2200	1	10	4	1	2
	209.3	6	1900	1	15	4	1	2
	252.3	4	2600	0	8	4	1	2
	192.9	4	1900	1	14	2	1	2.5
	209.3	5	2100	0	20	5	0	1.5
	345.3	8	2600	0	9	4	1	2
	326.3	6	2100	0	11	5	1	3
	173.1	2	2200	1	21	5	1	1.5
	187	2	1900	0	26	4	0	2
	257.2	2	2100	0	9	4	1	2
	233	3	2200	0	14	3	1	1.5
	180.4	2	2000	0	11	5	0	2
	234	2	1700	0	19	3	1	2
	207.1	2	2000	0	11	5	1	2
	247.7	5	2400	0	16	2	1	2
	166.2	3	2000	1	16	2	1	2
	177.1	2	1900	0	10	5	1	2
	182.7	4	2000	1	14	4	0	2.5
	216	4	2300	0	19	2	0	2
	312.1	6	2600	0	7	5	1	2.5
	199.8	3	2100	0	19	3	1	2
	273.2	5	2200	0	16	2	1	3
	206	3	2100	1	9	3	0	1.5
	232.2	3	1900	1	16	1	1	1.5
	198.3	4	2100	1	19	1	1	1.5
	205.1	3	2000	1	20	4	0	2
	175.6	4	2300	1	24	4	1	2
	307.8	3	2400	1	21	2	1	3
	269.2	5	2200	0	8	5	1	3
	224.8	3	2200	0	17	1	1	2.5
	171.6	3	2000	1	16	4	0	2
	216.8	3	2200	0	15	1	1	2
	192.6	6	2200	1	14	1	0	2
	236.4	5	2200	0	20	3	1	2
	172.4	3	2200	0	23	3	0	2
	251.4	3	1900	0	12	2	1	2
	246	6	2300	0	7	3	1	3
	147.4	6	1700	1	12	1	0	2
	176	4	2200	0	15	1	1	2
	228.4	3	2300	0	17	5	1	1.5
	166.5	3	1600	1	19	3	0	2.5
	189.4	4	2200	0	24	1	1	2
	312.1	7	2400	0	13	3	1	3
	289.8	6	2000	0	21	3	1	3
	269.9	5	2200	1	11	4	1	2.5
	154.3	2	2000	0	13	2	0	2
	222.1	2	2100	0	9	5	1	2
	209.7	5	2200	1	13	2	1	2
	190.9	3	2200	1	18	3	1	2
	254.3	4	2500	1	15	3	1	2
	207.5	3	2100	1	10	2	0	2
	209.7	4	2200	1	19	2	1	2
	294	2	2100	0	13	2	1	2.5
	176.3	2	2000	1	17	3	0	2
	294.3	7	2400	0	8	4	1	2
	224	3	1900	1	6	1	1	2
	125	2	1900	0	18	4	0	1.5
	236.8	4	2600	1	17	5	1	2
	164.1	4	2300	0	19	4	0	2
	217.8	3	2500	0	12	3	0	2
	192.2	2	2400	0	16	2	0	2.5
	125.9	2	2400	0	28	1	0	1.5
	220.9	2	2300	1	12	1	1	2
	294.5	6	2700	0	15	3	1	2
	244.6	2	2300	0	9	2	1	2.5
	199	3	2500	1	18	1	0	1.5
	240	4	2600	0	13	4	1	2
	263.2	4	2300	0	14	3	1	2
	188.1	2	1900	0	8	4	1	1.5
	243.7	6	2700	0	7	4	1	2
	221.5	4	2300	0	18	3	1	2
	175	2	2500	0	11	3	0	2
	253.2	3	2300	0	16	2	1	2
	155.4	4	2400	1	16	3	0	2
	186.7	5	2500	1	21	4	0	2.5
	179	3	2400	1	10	4	1	2
	188.3	6	2100	1	15	4	1	2
	227.1	4	2900	0	8	4	1	2
	173.6	4	2100	1	14	2	1	2.5
	188.3	5	2300	0	20	5	0	1.5
	310.8	8	2900	0	9	4	1	2
	293.7	6	2400	0	11	5	1	3
	179	3	2400	0	8	4	1	2
	188.3	6	2100	1	14	2	1	2.5
	227.1	4	2900	0	20	5	0	1.5
	173.6	4	2100	0	9	4	1	2
	188.3	5	2300	0	11	5	1	3