Question

(1 point) Holding everything else constant, which change to the sample size will reduce the width of a confidence interval for a population mean by half?

A. Raise the sample size to the power 4.
B. Double the sample size.
C. Square the sample size.
D. Quadruple the sample size.
E. Half the sample size.

Select True or False from each pull-down menu, depending on whether the corresponding statement is true or false.

  ?    True    False      1. We say that two samples are dependent when the selection process for one is related to the selection process for the other.

  ?    True    False      2. The pooled variances t−t−test requires that the two population variances are not the same.

  ?    True    False      3. In testing the difference between two population means using two independent samples, we can use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference x¯1−x¯2x¯1−x¯2 if the populations are normal with equal variances.

  ?    True    False      4. Independent samples are those for which the selection process for one is not related to the selection process for the other.

(1 point) A 90% confidence interval for the difference between the means of two independent populations with unknown population standard deviations is found to be (-0.2, 5.4).

Which of the following statements is/are correct? CHECK ALL THAT APPLY.

A. A two-sided two-sample tt-test testing for a difference between the two population means is rejected at the 10% significance level.
B. A two-sided matched-pairs tt-test testing for a difference between the two population means is rejected at the 10% significance level.
C. A two-sided two-sample tt-test testing for a difference between the two population means is not rejected at the 10% significance level.
D. The standard error of the difference between the two observed sample means is 2.6.
E. A two-sided matched-pairs tt-test testing for a difference between the two population means is not rejected at the 10% significance level.
F. None of the above.

(5 points) In a study to compare the IQ between boys and girls in a particular elementary school, a random sample of seventh grade boys and girls was taken from a Waterloo Elementary School. The girls and boys were asked to take an IQ test and their scores were recorded. Some summary statistics of the IQs of the boys and girls is given below.

Gender	Number of children measured	Average IQ	Standard deviations of IQ
Boys	17	107.1	5.6
Girls	15	105.5	4.9

Part a) What is the parameter of interest in this study?

The difference in the mean IQ of seventh grade grade boys and girls at the Waterloo Elementary School.
The difference in the mean IQ of the children taken in the sample from the Waterloo Elementary School.
The mean IQ of boys and girls at the Waterloo Elementary School.
The difference in the variances of IQ of the boys and girls taken in the sample from the Waterloo Elementary School.
The mean IQ of children at elementary schools in Canada.

Part b) Based on the data provided, what is your estimate of this parameter?  

Part c) In testing a hypothesis about the parameter of interest, what would your null hypothesis be?

There is a difference in the mean IQ for boys and girls at the Waterloo Elementary School.
There is no difference in the mean IQ for seventh grade boys and girls at the Waterloo Elementary School.
The difference between the mean IQ of seventh grade boys and girls is 1.6.
The mean difference between the IQ of a seventh grade boy at the Waterloo Secondary School and the IQ of a seventh grade girl at the same school is 1.6.
The mean IQ of seventh grade boys at the Waterloo Elementary School is greater than the mean IQ of seventh grade girls at the same school.

Part d) You would take the alternative hypothesis to be:

two-sided
one-sided, left-tailed
one-sided, right-tailed
it does not matter whether we take a one-sided or two-sided alternative
Part e) If you use a 5% level of significance, which of the following would you conclude?

There is sufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school.
There is sufficient evidence to suggest that the difference between the mean IQ of seventh grade boys and girls at the school is 1.6.
There is sufficient evidence to suggest that the mean difference between the IQ of a seventh grade boy at the school and the IQ of a seventh grade girl at the school is 1.6.
There is sufficient evidence to suggest that the mean IQ of seventh grade boys at the school is greater than the mean IQ of seventh grade girls at the school.
There is insufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school.
There is insufficient evidence to suggest that the difference between the mean IQ of seventh grade boys and girls at the school is 1.6.
There is insufficient evidence to suggest that the mean difference between the IQ of a seventh grade boy at the school and the IQ of a seventh grade girl at the school is 1.6.
There is insufficient evidence to suggest that the mean IQ of seventh grade boys at the school is greater than the mean IQ of seventh grade girls at the school.

(4 points) A sample of 2222 randomly selected student cars have ages with a mean of 7.67.6 years and a standard deviation of 3.63.6 years, while a sample of 1818 randomly selected faculty cars have ages with a mean of 55 years and a standard deviation of 3.33.3 years.

1. Use a 0.010.01 significance level to test the claim that student cars are older than faculty cars.

(a) The test statistic is

(b) The critical value is

(c) Is there sufficient evidence to support the claim that student cars are older than faculty cars?

A. No
B. Yes


2. Construct a 9999% confidence interval estimate of the difference μs−μfμs−μf, where μsμs is the mean age of student cars and μfμf is the mean age of faculty cars.
--------------<(μs−μf)-(μs−μf)<----------------

Select True or False from each pull-down menu, depending on whether the corresponding statement is true or false.

  ?    True    False      1. If a sample of size 30 is selected, the value AA for the probability P(−A≤t≤A)=0.95P(−A≤t≤A)=0.95 is 2.045.

  ?    True    False      2. If a sample has 18 observations and a 90% confidence estimate for μμ is needed, the appropriate t-score is 1.740.

  ?    True    False      3. If a sample of size 250 is selected, the value of AA for the probability P(−A≤t≤A)=0.90P(−A≤t≤A)=0.90 is 1.651.

  ?    True    False      4. If a sample has 15 observations and a 95% confidence estimate for μμ is needed, the appropriate t-score is 1.753.

(9 points) From previous studies, it has been generally believed that Northern Hemisphere icebergs have a mean depth of 270 meters. An environmentalist has suggested that global warming has caused icebergs to have greater depth. A team of scientists visiting the Northern Hemisphere observed a random sample of 41 icebergs. The depth of the base of the iceberg below the surface was carefully measured for each. The sample mean and standard deviation were calculated to be 276 meters and 20 meters respectively.

Part a) What is the parameter of interest relevant to this hypothesis test?

A. 41
B. The mean depth (in m) of the 41 icebergs in the study.
C. The mean depth (in m) of all Northern Hemisphere icebergs.
D. 270 meters
E. None of the above

Part b) In testing a hypothesis about a parameter of interest, what would your null hypothesis be?
The mean depth of the Northern Hemisphere icebergs is 270 meters now.
The mean depth of the Northern Hemisphere icebergs is greater than 270 meters now.
The mean depth of the Northern Hemisphere icebergs is smaller than 270 meters now.
The mean depth of the Northern Hemisphere icebergs is different from 270 meters now.
The mean depth of the Northern Hemisphere icebergs used to be 270 meters.
The mean depth of the Northern Hemisphere icebergs used to be greater than 270 meters.
The mean depth of the Northern Hemisphere icebergs used to be smaller than 270 meters.
The mean depth of the Northern Hemisphere icebergs used to be different from 270 meters.

Part c) You would take the alternative hypothesis to be:
one-sided, right-tailed.
two-sided.
one-sided, left-tailed
it does not matter whether we take a one-sided or two-sided alternative.

Part d) Compute the test statistic (Please round your answer to three decimal places):

Part e) Assume all necessary conditions are met (random sampling, independence samples, large enough sample size). Which of the following approximate the sampling distribution of the test statistic in Part d:
Normal distribution
t-distribution

Part f) Which of the following ranges the P-value must lie in? [You will need the t-table to answer this question.]

A. <0.005
B. 0.05-0.01
C. 0.01-0.025
D. 0.025-0.05
E. 0.05-0.10
F. >0.10

Part g) Based on the PP-value that was obtained, you would (Select all that apply):

A. reject the null hypothesis at α=0.05α=0.05 level of significance
B. neither reject nor accept the null hypothesis.
C. fail to reject the null hypothesis at all.
D. believe the null hypothesis is true.
E. reject the null hypothesis at α=0.1α=0.1 level of significance
F. None of the above

Part h) Suppose that, based on data collected, you reject the null hypothesis. Which of the following could you conclude?
There is sufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
There is sufficient evidence to suggest that the mean depth of the Northern Hemisphere icebergs has not changed.
There is sufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has decreased due to global warming.
There is insufficient evidence to suggest that the mean depth of the Northern Hemisphere icebergs has not changed.
There is insufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
There is insufficient evidence to suggest that the mean depth of Northern Hemisphere icebergs has decreased due to global warming.

Part i) Suppose that, based on data collected, you decide that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
it is possible that you are making a Type I error.
it is possible that you are making a Type II error.
it is certainly correct that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
it is certainly incorrect that the mean depth of Northern Hemisphere icebergs has increased due to global warming.
there must have been a problem with the way the sample was obtained.

(2 points) Suppose you have selected a random sample of n=13n=13 measurements from a normal distribution. Compare the standard normal zz values with the corresponding tt values if you were forming the following confidence intervals.

(a)    95% confidence interval
z=
t=

(b)    90% confidence interval
z=
t=

(c)    99% confidence interval
z=
t=

Answer 1

please post the remaining questions separately.