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WorksheetsStatistics Chapter 8.1 & 8.2 Review
Total questions: 40
Worksheet time: 53mins
Name
Class
Date
1.
Calculate the confidence interval for the population mean at the given level of confidence: n = 65, σ = 3.14, x = 19.5, c = 0.80
a)
(18.5, 20.5)
b)
(19, 20)
c)
(19.001, 19.999)
d)
(18.9, 19.8)
2.
Calculate the confidence interval for the population mean at the given level of confidence: n = 846, σ = 1.04, x = 7.9, c = 0.90
a)
(7.8412, 7.9588)
b)
(6.999, 7.859)
c)
(8.844, 9.544)
d)
(5.999, 6.859)
3.
If the confidence level is 90%, what is the associated critical z value (Za/2)?
a)
2.557
b)
-1.645
c)
1.645
d)
-2.557
4.
If a sample of 225 students have a mean test score of 90, what is the point estimate?
a)
90.5
b)
91
c)
90
d)
90.1
5.
What is required to create a t-distribution?
a)
Population mean and sample mean
b)
Population distribution and sample size
c)
Z-interval
d)
Confidence interval
6.
If 656 randomly selected people spend a mean of $86 per week on lunch. What is the best point estimate for the mean amount of money spent per week on lunch for all 656 people?
a)
$86
b)
$67
c)
$80
d)
$68
7.
Value of t0.025 for a t-distribution with 25 degrees of freedom.
a)
-2.060
b)
2.060
c)
1.555
d)
-1.555
8.
The mean number of cookies in a household per family per week for a random sample of 786 families in the state of New York is 67.9 cookies. What is the best point estimate?
a)
68
b)
78
c)
86
d)
87
9.
What is a critical Z-Value?
a)
The boundaries for the area of c under the middle of the standard normal curve.
b)
Determines the Z-value
c)
The mean of a t-distribution
10.
How do you find the lower bound margin of error?
a)
Subtract E from the X value
b)
Use the Z interval
c)
Subtract the mean from the confidence value
d)
Add E to the the X value
11.
Your boss comes in and wants to know how many people he should sample if there is a standard deviation of 8.67. He wants to be 98% confident with a 0.1 maximum error. What is the minimum sample size required to construct the confidence interval with the desired characteristics?
a)
40,808
b)
41,000
c)
39,000
d)
20,000
12.
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $16.6 for a random sample of 7472 people. Assume the population standard deviation is known to be 11$. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
a)
16.3 to 16.9
b)
16.2 to 16.8
c)
16.1 to 16.7
d)
15.8 to 16.4
13.
Consider the value of t such that 0.025 of the area of the curve is to the right of t. With the degrees of freedom being 9, what is the value of t?
a)
2.262
b)
-2.262
c)
1.557
d)
-1.557
14.
True or False: the four pieces of information required to construct a confidence interval for the population mean is number of people, standard deviation, confidence level, and sample mean.
a)
True
b)
False
15.
Consider the value of t such that 0.01 of the area under the curve is to the right of t. Assuming the degrees of freedom equals 21, select the t value from the t table.
a)
2.518
b)
-2.518
c)
1.857
d)
-1.857
16.
Consider the value of t such that 0.05 of the area under the curve is to the left of t. Assuming the degrees of freedom is 16, what is the value of t.
a)
-1.746
b)
1.746
c)
2.557
d)
-2.557
17.
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $21.9, and the variance is known to be $31.36. How large of a sample would be required in order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.26?
a)
1257
b)
1255
c)
1258
d)
1260
18.
A researcher is looking to estimate the mean LSAT score of law school applicants who completed their undergraduate degrees at small liberal arts colleges. She wants a 99% level of confidence and a maximum margin of error of 2 points. How many applicants must she survey if previous studies show the standard deviation to be approximately 9 points?
a)
138 applicants
b)
139 applicants
c)
135 applicants
d)
133 applicants
19.
From a random sample of 49 stray dogs, a veterinarian finds that their mean weight is 41.0 pounds with a standard deviation of of 8.5 pounds. Construct and interpret a 98% confidence interval for the mean weight of all stray dogs in this area.
a)
(37.1, 42.9)
b)
(38.1, 43.9)
c)
(36.1, 39.9)
d)
(39.1, 44.9)
20.
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.13 gallons. A previous study found that for an average family the variance is 2.56 gallons and the mean is 16.3 gallons per day. If they are using a 80% level of confidence, how large of a sample is required to estimate the mean usage of water?
a)
250
b)
249
c)
248
d)
246
21.
True or false: you need to know the standard deviation to calculate t distributions.
a)
True
b)
False
22.
True or false: There is no standard t-distribution.
a)
True
b)
False
23.
True or false: The margin of error and the standard deviation are the same thing.
a)
True
b)
False
24.
Find the value of t0.05 with 15 degrees of freedom.
a)
1.443
b)
2.357
c)
1.625
d)
1.753
25.
Determine the confidence interval if the population size is 89, the standard deviation 2.01, the confidence level is 0.95, and a population mean of 45.
a)
(46.58, 47.42)
b)
(45.58, 46.42)
c)
(44.58, 45.42)
d)
(43.58, 44.42)
26.
True or False: A t-distribution curve is not symmetrical or bell curved.
a)
True
b)
False
27.
How many parameters does t-distribution have?
a)
One
b)
Two
c)
Three
d)
Four
28.
Find the value of t0.010 with 25 degrees of freedom.
a)
2.485
b)
-2.485
c)
1.557
d)
-1.557
29.
Mrs. Elston wants to estimate the mean spending habits per month for MOT students. The mean is found to be $200 for a random sample of 75 students. We assume the standard deviation is $10. What would the confidence intervals be for 90%? (round decimals to two places).
a)
(199.2 , 202.9)
b)
(198.2 , 201.9)
c)
(197.2 , 200.9)
d)
(196.2 , 199.9)
30.
A bakery of 67 chefs on average can make .75 cakes per half hour. If the margin of error in a 99% confidence level is .50, what is the confidence interval?
a)
(.75, 1.75)
b)
(.50, 1.50)
c)
(.25, 1.25)
d)
(.45, 1.45)
31.
A scientist wants to know how many times per hour a strand of bacteria reproduces. There is a mean of 6.3 reproductions and the standard deviation is 2.2. If a sample of 987 was used for the study, construct a 90% confidence interval for the true mean number of reproductions per hour for the bacteria. Round answers to one decimal place.
a)
Lower Endpoint: 6.2, Upper Endpoint: 6.4
b)
Lower Endpoint: 6.1 Upper Endpoint: 6.4
c)
Lower Endpoint: 6.3 Upper Endpoint: 6.5
d)
Lower Endpoint: 6.1 Upper Endpoint: 6.5
32.
An energy company wants to know the mean household electricity usage by its customers in kWh each day. They would like the estimate to have a maximum error of 0.12 kWh. A previous study found that for average families the standard deviation is 22 kWh, and the mean is 18.9 kWh per day. If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of electricity?
a)
600 families
b)
573 families
c)
576 families
d)
580 families
33.
Calculate the margin of error for the following confidence interval:
14.53 < µ < 18.23
14.53 < µ < 18.23
a)
1.86
b)
1.85
c)
1.87
d)
1.89
34.
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. He believes that the mean income is $32.0, and the variance is known to be $144.00. How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.75?
a)
984
b)
987
c)
989
d)
986
35.
The mean heating bill for 40 residents of a Middletown apartment building is $70. What is the best point estimate for the mean heating bill for all residents of the apartment building?
a)
$70.00
b)
$70.01
c)
$70.10
d)
$71.00
36.
The school board administered an IQ test to 25 randomly selected teachers. They found that the average IQ score was 115 with a standard deviation of 11. Assume that the cumulative probability is 0.90. What population mean would have produced this sample result?
a)
112.2
b)
112.1
c)
112.3
d)
112.5
37.
True or False: The margin of error is just another way to represent standard deviation.
a)
True
b)
False
38.
True or False: When the population standard deviation is unknown, it can be estimated by dividing the approximate range of the variable by three.
a)
True
b)
False
39.
Consider the value of t such that the area under the curve between − ∣t∣ and ∣t∣ equals 0.90.
a)
1.796
b)
1.797
c)
1.795
d)
1.801
40.
Consider the value of t such that the area under the curve between −∣t∣and ∣t∣equals 0.90. Select the graph which best represents the given description of t.
a)
The upper left graph
b)
The upper right graph
c)
The bottom left graph
d)
The bottom right graph
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