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WorksheetsSummative Test in Statistics and Probability
Total questions: 25
Worksheet time: 14mins
Which of the following values do we need to define the sampling distribution?
probability
standard deviation
Statistic
parameter
How can the standard error be reduced in surveys?
by decreasing the population size
by decreasing the sample size
by increasing the sample size
by increasing the population size
The average lot size of the houses in a small village is 55 square meters with a standard deviation of 10 square meters. Find the mean of the sampling distribution of the sample mean with a sample size of 50 houses if lot sizes are normally distributed.
10
50
55
60
Find the standard error of the sampling distribution of the sample mean if n=75 and σ=500.
57.74
425
6.67
0.3
A normal population has a mean of 100. Find the standard error of the sampling distribution of the sample mean of a normal population with a sample size of 100 if the population standard deviation is equal to 10% of the population mean.
1
100
10
0.1
Which of the following is true about the mean of the sampling distribution of the sample mean if the population mean is unknown?
It is approximately equal to the mean of a single sample.
It is approximately equal to the mean of a single sample divided by the sample size.
It is equal to the mean of a single sample divided by the sample size.
It is equal to the mean of a single sample.
What is in the center of the sampling distribution?
true sample mean
variance
standard deviation
true population mean
A shipping company measured the weight of a sample of 50 boxes in its warehouse. The average weight of the boxes is 25 kg with a standard deviation of 12 kg. Estimate the mean of the sampling distribution of the sample mean if the weights follow a normal distribution.
25 kg
1250 kg
1.7 kg
12 kg
What is the standard error of the mean if a sample of 400 units has a mean of 15 and a standard deviation of 2? Assume that the population is normally distributed.
0.13
0.005
15
0.1
Four students took an exam in mathematics and got the following scores: 7, 12, 19, and 21. What is the mean of the sampling distribution of the sample mean with a sample size of 2?
14.75
14.5
13.75
13.5
What does it imply when the sample mean is approximately equal to the population mean?
Solving for the sample mean is not necessary.
Population mean should always be solved.
Population mean is a good estimate for the mean of any sample.
Sample mean is enough to represent the population mean.
A survey statistician wants to decrease the standard error of the mean of his study by half. What should he do to the sample size?
Quadruple the sample size
Decrease the sample size by half
It is not possible to decrease the estimated standard error by half.
Double the sample size
If samples of size 100 are selected from a population with a mean of 18 and a standard deviation of 28, what is the standard error of the mean?
2.8
10
4.6
1.8
Multiple samples with a size of 35 are taken from a known population, where μ=25 and σ=4. As the sample size increases, what should be the value of the mean of sample means approximate?
2
12.5
25
35
A researcher wants to take random samples of size 40 of a certain population with a mean of 23.5 and a variance of 18.49. What is the approximate standard deviation of sample means?
0.68
5.47
3.72
4.3
Members of the urban poor receive an average of ₱110 per day with a standard deviation of ₱20. If a random sample of 25 people is taken, what is the approximate mean of the sampling distribution?
₱25
₱45
₱55
₱110
According to the Central Limit Theorem, the sampling distribution of the sample mean is normal given that large sample sizes are taken. What is the expected shape of the sampling distribution?
bell-shaped
uniform
skewed
U-shaped
If the population is skewed, then the sample size n must be ______.
larger
smaller
normal
equal to 30
When we say that size n must be larger, that means n should be ________.
at least 30
equal to 30
at most 30
greater than 30
When does the sampling distribution of x becomes approximately normal for relatively small values of n?
If the population is skewed
If the population is normal
If the population increases
If the population is approximately symmetric
Which of the following is true about the sampling distribution of the sample mean of a normally distributed population?
The sampling distribution is flat.
The sampling distribution is skewed.
The sampling distribution is not normally distributed.
The sampling distribution is also normally distributed.
As n increases, the distribution becomes normal. What is its basis?
the Central Limit Theorem
the population variance
the sample mean
the population mean
Which of the following distributions is used to estimate population parameters when the size of the provided sample is small?
t-distribution
z-distribution
sampling distribution
frequency distribution
A study shows that 80% of students in a school love to listen to music while studying, with a sampling error of ±3%. What does this imply?
The actual proportion of students listening to music while studying is 3%.
The actual proportion of students listening to music while studying is between 77% and 83%.
The actual proportion of students listening to music while studying is either 3% or 80%.
The actual proportion of students listening to music while studying is equal to both 77% and 83%.
A researcher decided to gather data from all 150 employees in a certain office instead of just selecting certain number of people among them. What sample strategy did he use?
similar studies
random sampling
systematic sampling
census for small populations
