1.[1pt, 0.25pts each] TRUE OR FALSE. Write the full word True or False underneat
ID: 3355231 • Letter: 1
Question
1.[1pt, 0.25pts each] TRUE OR FALSE. Write the full word True or False underneath each statement
a.It is possible for the standard error to be larger than the population standard deviation.
b.A normal population has a mean of 70 and a standard deviation of 10. It is more likely to obtain a score of 72 with a sample size of 25 than it is to obtain a score of 80 with a sample size of 25.
c.If a population distribution is normal, you need a sample size of at least 30 to make sure your sampling distribution approximates normality.
d.Decreasing the sample size of will cause the standard error of to get smaller.
2.[1.5pts: 0.25pts each] A population has a mean of = 100 and a standard deviation of = 20. Find the z-score corresponding to each of the following sample means obtained from this population.
= 102 for a sample of n = 4 scores
= 102 for a sample of n = 100 scores
= 95 for a sample of n = 16 scores
= 95 for a sample of n = 25 scores
Using z-scores, find the upper and lower boundaries that separate the middle 95% of the sample means from the extreme 5% in the tails of the distribution (n = 25)
A sample mean of = 106 is computed for a sample of n = 25 scores. Is this sample mean in the extreme 5%?
3.[1pt: 0.25pts each] For a normal population with = 70 and = 20, what is the probability of obtaining a sample mean greater than 75
for a random sample of n = 4 scores?
for a random sample of n =16 scores?
for a random sample of n = 40 scores?
for a random sample of n = 100 scores?
4. [1pt: 0.25pts each] A normal population has = 70 and = 12.
What proportion of the scores have values lower than 65?
What proportion of the sample means have values lower than 65 for samples of size n = 25?
What proportion of the scores have values greater than x = 73?
What proportion of the sample means have values greater than 73 for samples of size n = 16?
5.[2.5pts: a and c: 0.5pts each; b and d: 1pt each] People are selected to serve on juries by randomly picking names from the list of registered voters. The average age for registered voters in the country is = 39.7 years with = 11.8. The distribution of ages is approximately normal.
During a recent jury trial in the country courthouse, a statistician noted that the average age for the 12 jurors was = 50.4 years.
What is the probability of getting a jury with this average age or older by chance?
Is it reasonable to conclude that this jury was selected by a random sample of registered voters? Why?
During another recent jury trial in the country courthouse, a statistician noted that the average age for the 12 jurors was = 30.2 years.
What is the probability of getting a jury with this average age or younger by chance?
Is it reasonable to conclude that this jury was elected by a random sample of registered voters? Why?
Find the 90th percentile for the age of an individual jury member in the full population.
Find the 90th percentile for the average age of jury members (n = 12).
Explanation / Answer
1.
A) False, standard error is given as s/sqrt(n) here n is always positive so standard error cannot be less than s
B) z for 72 is (72-70)/(10/sqrt(25))=1 and z for 80 is (80-70)/(10/sqrt(25))=5, True as first score is closer to mean
C) True
D) False, standard error is given as s/sqrt(n), so as sample size decreases, standard error increases
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