Question 1
Suppose we want to test Ho: μ-80 against H₂:μ * 80 based on a random sample
of 50 observations, with a sample mean 86. Given that the population is normally
distributed with a standard deviation of 16.
Check all of the correct decisions:
Do not reject Ho at α = -0.001.
Reject Ho at α =0.01.
Do not reject Ho at α = -0.01.
Reject Ho at α = 0.001.
Do not reject Ho at α =0.05.
Question 2
Which statements are correct? Please select all of the correct answers.
In hypothesis testing, if the p-value of a test is very large, we accept the null
hypothesis and reject the alternative hypothesis.
In hypothesis testing, if the p-value of a test is less than 0 that means there is
extremely strong evidence against the null hypothesis.
As the probability of Type II Error increases, the power of a hypothesis test
decreases.
In hypothesis testing, if the test statistic is in the rejection region, then we reject
the null hypothesis.
A report claimed that the mean height of maple trees in Ontario is 30m. Suppose the
researchers suspected that the mean height might exceed 30m and they wanted to
see if they had strong evidence of this.
The data below recorded the height (in meters) of a random sample of 15 maple
trees measured in Ontario.
30, 31, 28, 26, 39, 32, 21, 17, 33, 25, 39, 40, 42, 36, 36
(The following four questions depend on this information.)
Question 3
Which of the following is the most appropriate null and alternative hypotheses?
Ho:µ=30 vs H₂: µ ≠ 30
Ho: µ=30 vs H₂: μ> 30
Ho:x = 30 vs H₂: x ≠30
Ho: µ = 29.3 vs H₂: μ> 29.3
Ho: µ=29.3 vs H₂: x > 29.3
Question 4
What is the value of the appropriate test statistic?
Enter your answer to 3 decimal places in the space below.
Question 5
What is the p-value of the test?
Enter your answer to 3 decimal places in the space below. Do not enter any units.
Question 6
Which of the following is the most appropriate conclusion at the 5% significance
level?
i. There is insufficient evidence to reject the null hypothesis. We conclude that the
mean height of maple trees in the sample is 30m.
ii. There is insufficient evidence to reject the null hypothesis. We conclude that the
true mean height of maple trees in Ontario is not greater than 30m.
iii. There is sufficient evidence to reject the null hypothesis. We conclude that the
true mean height of maple trees in Ontario is greater than 30m.
iv. There is sufficient evidence to reject the null hypothesis. We conclude that the
mean height of maple trees in the sample is greater than 30m.
Question 7
A 95% confidence interval for the mean of a certain population was calculated to be
(20.98, 40.23). Consider the following statements:
I. In repeated sampling, we would expect 95% of similarly constructed confidence
intervals to contain the population mean.
II. In repeated sampling, we would expect 95% of the sample means to fall in this
confidence interval.
III. We are 95% confident that true mean lies within this confidence interval.
Which of these statements are TRUE?
I and II only
I and III only
All three of the statements are true.
I only
II and III only
Question 8
Suppose we are sampling from a normally distributed population.
x =10, 0=12, and n-20.
What is the 99% margin of error?
(Please choose the closest answer)
06.81
06.91
06.24
7.68
07.13
Question 9
What is a Type Il error?
It is when one does not reject Ho when in fact it is false.
It is when one rejects H, when in fact it is It false.
It is when one rejects Ho when in fact it is true.
It is when one rejects Ho when in fact it is false.
It is when one rejects H, when in fact it is true
Question 10
Consider the sample 77, 68, 48, 51, 75, 69, 45, 73, 60 from a normal population
with population mean µ and population variance a². Find the 90% confidence
interval for u.
(Please choose the closest answer.)
(45.80, 80.10)
(55.29, 70.49)
(60.12, 78.82)
(57.18, 68.60)
(40.23,75.63)
Question 11
A limnologist wishes to estimate the mean length of young trout in a lake.
What is the minimal number of young trouts required in a random sample so the
probability is 0.95 that the sample mean will fall within 2mm of the true mean?
(Assume length of young trout are normally distributed with g=10mm)
Question 12
Suppose we want to test Ho: = 80 against H₂: µ ≠ 80 based on a random sample
of 50 observations, with a sample mean 86. Given that the population is normally
distributed with a standard deviation of 16.
What is the value of the appropriate test statistic?
Enter your answer to 3 decimal places in the space below.
