There are 218 first-graders in an elementary school. Of these first graders, 86 are boys and 132 are girls. School wide, there are 753 boys and 1063 girls. The principal would like to know if the gender ratio in first grade reflects the gender ratio school wide. a. Identify the hypothesis. b. What are the degrees of freedom (df)? c. Complete this table in SPSS and paste the output below to replace it: Men Women No. Observed No. Expected No. Observed No. Expected d. Calculate χ² in SPSS and paste the output below. e. Can you reject the null hypothesis at α = .05? Explain why or why not. c. Complete this table in SPSS and paste the output below to replace it: Men Women No. Observed No. Expected No. Observed No. Expected d. Calculate χ² in SPSS and paste the output below. e. Can you reject the null hypothesis at α = .05? Explain why or why not.

how do you set this up in SPSS?

There are three different types of tests we learned. What one of the three types is the following? “ A researcher estimates that high school girls miss more days of school than high school boys. A sample of 16 girls showed that they missed an average of 3.9 days of school and a sample of 22 boys showed that they missed an average of 3.6 days. The standard deviation of the 16 girls was .6 and the standard deviation of the boys was .8. Using an alpha level of .01, test the researchers claim.

select the conclusion that should be drawn in step 4. Select one: a. Reject Ho b. Do not reject Ho

The critical value for this problem is: Select one: a. 2.576 b. 2.602 c. 2.947 d. 2.326 e. None of the choices

The degree of freedom for this test where we are assuming that the variances are unequal is: Select one: a. 21 b. 35 c. 16 d. 15 e. 22

The final result from this test is: Select one: a. Evidence supports the claim. b. Evidence does not support the claim

The p-value for this test is: Select one: a. .12 b. .04 c. .01 d. .10 e. .24

The test value to the nearest hundredth is: Select one: a. 1.39 b. 1.32 c. 1.82 d. 2.16 e. None of the choices

Using the problem in question two, the alternate hypothesis for the statistical test would be:

Select one: a. muG < muB (claim) b. muG < muB c. muG > muB (claim) d. muG > muB

(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.

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=

Gender in a Children’s Toy Store.

1) Can you detect a boys’ section and a girls’ section? How do you know?

2) How do the toys in the boys’ section and girls’ section differ? (Pay attention to number of toys, types of toys, content of the games, etc.)

3) How are the toys in the boys’ section and girls’ section similar?

What sorts of interactions with other children do the boys’ and girls’ toys encourage? (For example, competition or cooperation? Independence or dependence? Emotional intimacy or distance?)

4) Which toys (boys’, girls’, or both) are designed for active play? Which seem to encourage passive play?

5)For what sorts of adult roles do the boys’ and girls’ toys prepare children?

6) How might these kinds of toys influence boys’ sexual attitudes and behaviors?

7)How might these kinds of toys influence girls’ sexual attitudes and behaviors?

8)How do these observations relate to the social construction of gender?

6. (a).

In a particular town 10% of the families have no children, 30% have one child, 20% have
two children, 40% have three children, and 0% have four. Let T represent the total
number of children, and G the number of girls, in a family chosen at random from this
town. Assuming that children are equally likely to be boys or girls, find the distribution
of G. Display your answer in a table and sketch the histogram.

(b). Find E(T | G=1) = conditional expectation of number of children T, given 1 girl.

(c). Find the sum over k= 0, , 2, 3 of

E (T | G=k) P( G= k).

HINT: The hard way is to compute both factors of all 4 terms and do the arithmetic. The easy way is to use the R.A.C.E.

After a campaign to encourage students to take precautions against skin cancer, in a certain high school class consisting of 34 girls and 39 boys, it is observed that 26 girls and 25 boys take precautions as measured by a survey to elicit how often they wear sunscreen, sunglasses and hats for protection against the sun.

Please use this information to calculate the probabilities for the following questions. Please provide each numerical answer to TWO DECIMAL places (X.XX) with no additional information in the answer box. Just X.XX (i.e. no extra spaces, no units, etc).

What is the probability that a student picked at random takes precautions against skin cancer (by wearing sunscreen, sunglasses and a hat), given that the student is a boy?

One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples and calculate the given summary statistics of the boys and the girls for comparable math classes. In Calculus, 15 boys had a mean percentage of 82.3 with standard deviation of 5.6 while 12 girls had a mean percentage of 81.2 with standard deviation of 6.7. What assumptions need to be made in order to determine the 90% confidence interval for the difference in the mean percentage scores for the boys in calculus and the girls in calculus? Supposing the assumption is true, calculate the interval.

Wainer (1997) presented data on the relationship between hours of TV watching and mean score on the 1990 National Assessment of Educational Progress (NAEP) for eighth-grade mathematics assessment. The data follow, separated for boys and girls.

1. Plot the relationship between Hours Watched and NAEP math scores separately for boys and girls.
2. Find and interpret the slope and intercept for these data, again keeping boys and girls separate.

There are 12 students in a party. Five of them are girls. In how many ways can these 12 students be arranged in a row if (i) there are no restrictions? (ii) the 5 girls must be together (forming a block) (iii) no two girls are adjacent? (iv) two particular boys A and B, there are no boys but exactly 3 girls?

1. Discuss the special risks of addiction for boys that differ from the special risks for girls. Should there be gender-specific programming for girls and why?


2. Identify risk factors for substance and other addictions at each stage of the lifecycle. Which stage holds the most risks and why?


3. Reminisce about your experience (whether personal or someone you know) with alcohol and other drugs (including steroids in high school) and what you have learned which can be imparted to the next generation.