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WorksheetsEstimation
Total questions: 50
Worksheet time: 2hrs 37mins
Parameters are
numerical characteristics of a sample.
numerical characteristics of a population.
the averages taken from a sample.
numerical characteristics of either a sample or a population.
Sampling distribution ΣXi/n is
probability distribution of the sample average
probability distribution of the sample proportion.
mean of the sample.
mean of the population
A simple random sample of 100 observations was taken from a large population. The sample average and the sample standard deviation were determined to be 80 and 12 respectively. The standard deviation of the sample average is
1.20
0.12
8
0.8
A simple random sample of 144 observations was taken from a large population. The sample average and the sample standard deviation were determined to be 1234 and 120 respectively. The standard deviation of the sample average is
1234±120
120
1440
10
The following data was collected from a simple random sample of a population.
13 15 14 16 12
The mean of the population
is 14.
is 15.
is 15.1581
could be any value.
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is
0.4664
0.9328
0.0336
0.0672
Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample average for this situation?
Approximately normal because the sample size is small relative to the population size
Approximately normal because of the central limit theorem
Exactly normal
None of these alternatives is correct
The following data was collected from a simple random sample of a population.
13 15 14 16 12
The point estimate of the population standard deviation is
2.5
1.581
2.
1.414
A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is
8.225
8.3
9.8
9.92
The t value for a 95% confidence interval estimation with 24 degrees of freedom is
1.711
2.064
2.492
2.069
A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The value of the margin of error at 95% confidence is
80.83
7.0
0.81
1.58
A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?
We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.
We are 95% confident that the interval (150, 350) captures the true average caloric content.
We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.
None of these are correct.
A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...
The t distribution is more accurate than a z distribution.
Clarity ratings for the entire bacth are normally distributed.
The t-distribution will create a narrower interval than z.
The standard deviation for the population is unknown.
Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.
89.08 < μ < 94.92
87.27 < μ < 96.73
87.29 < μ < 96.71
87.77 < μ < 96.23
In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a standard deviation of $950. Construct a 99% confidence interval for the repair cost for the population.
(1070, 2530)
(1273, 2326)
(1799, 1801)
(1776, 1823)
An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.
Find the critical value.
0.90
1.155
1.645
±1.645
The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.
What is the Confidence Interval to one decimal place?
(114.5, 125.6)
(112.8, 127.4)
(112.82, 127.38)
(114.56, 125.64)
A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?
60
75
90
180
Find the margin of error if confidence interval is 95%, standard deviation is 56, and sample size is 27.
21.123
20.345
2.056
25
A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?
We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.
We are 95% confident that the interval (150, 350) captures the true average caloric content.
We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.
None of these are correct.
Previous studies show that the standard deviation for work time is 3 hours, and a survey of 40 students has a mean of 9.8 work hours per week.
The 95% confidence interval is…
(8.84, 10.76)
(8.87, 10.73)
(9.02, 10.58)
(9.00, 10.60)
The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch.
If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31.8 inches?
99.7%
13.5%
16%
2.5%
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.
About what percent of the products last less than 9 days?
68%
34%
16%
2.5%
Given a mean of 75 and a standard deviation of 7, what percentage of scores are between 54 and 96?
34%
99.7%
95%
2.5%
Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 61 and 89?
475
400
340
80
Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 82?
475
170
237
80
68% of the marks in a test are between 51 and 64
Assuming this data is normally distributed, what are the mean and standard deviation?
Mean = 57
S.D. = 6.5
Mean = 57
S.D. = 7
Mean = 57.5
S.D. = 6.5
Mean = 57.5
S.D. = 13
The mean July daily rainfall in Hulu Kinta is 10 mm and the standard deviation is 1.5 mm
Assume that this data is normally distributed.
How many days in July would you expect the daily rainfall to be less than 8.5 mm?
5
6
7
10
434 Company pack coffee in bags marked as 250 g
A large number of packs of coffee were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively.
Assuming this data is normally distributed, what percentage of packs are underweight?
2.5%
3.5%
4%
5%
Students pass a test if they score 50% or more.
The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.
Assuming this data is normally distributed, what percentage of students pass the test? in percentage...
5
16
24
32
The ages of the population of people living in Meru area in Ipoh are Normally distributed with mean 43 and standard deviation 14
The town has a population of 5,000.
How many would you expect to be aged between 22 and 57?
You can use this Standard Normal Distribution curve:
1750
3860
3870
4330
