In a sample of families with 6 children each, the distribution of boys and girls is as shown in the following table:

Part A) Calculate the chi-square value to test the hypothesis of a boy-to-girl ratio of 1:1. (Express your answer using three decimal places)

Part B) Are the numbers of boys to girls in these families consistent with the expected 1:1 ratio? Yes or No

Part C) Calculate the chi-square value to test the hypothesis of binominal distribution in six-child families. (Express your answer using three decimal places)

Part D) Is the distribution of the numbers of boys and girls in the families consistent with the expectations of binomial probability? Yes or No

The average amount of time boys and girls aged 7 to 11 spend playing sports each day is believed to
be the same. A study is done and data are collected, resulting in the data in the following table.

a. Define the appropriate parameter(s) and state the hypotheses for testing if this study provides evidence that the mean amount of time boys and girls aged 7 to 11 play sports each day differs.

b. Set each of the hypotheses equal to zero and find the null value.a. Define the appropriate parameter(s) and state the hypotheses for testing if this study
provides evidence that the mean amount of time boys and girls aged 7 to 11 play sports each day
differs.

Researchers in a populous country contacted more than​ 25,000 inhabitants aged 25 years to see if they had finished high​ school; 88.5 % of the 12, 499 males and 80.7​% of the 12, 846 females indicated that they had high school diplomas.

​a) What assumptions are necessary to satisfy the conditions necessary for​ inference?

​b) Create a 99​% confidence interval for the difference in graduation rates between males and​ females, p Subscript males Baseline minus p Subscript females.

​c) Interpret your confidence interval.

​d) Is there evidence that boys are more likely than girls to complete high​ school?

10-1

Researchers in a populous country contacted more than​ 25,000 inhabitants aged 22 years to see if they had finished high​ school; 81.7%

of the 12,858 males and 80.1​% of the 12,957 females indicated that they had high school diplomas.

​a) What assumptions are necessary to satisfy the conditions necessary for​ inference?

​b) Create a 90​% confidence interval for the difference in graduation rates between males and​ females,

p Subscript males Baseline minus p Subscript femalespmales−pfemales.

​c) Interpret your confidence interval.

​d) Is there evidence that boys are more likely than girls to complete high​ school?

In families with four children, you're interested in the probabilities for the different possible numbers of girls in a family. Use theoretical probability (assume girls and boys are equally alike),compile a five -column table with the headings, O through 4, for the five possible numbers of girl children in a four child family. Then using G for girls and B for Boys, list under each heading the various birth order ways of achieving that number of girls in a family. Use table to calculate the following probabilities:

1. The probability of 1 girl.

2. The probability of 2 girls.

3. The probability of 4 girls.

4. The probability the third child born is a girl.

The probability of 4 girls

How many ways can you arrange 5 boys and 6 girls alternately in a row of 12 seats? An empty seat between 2 boys is not allowed. As it is so for 2 girls.

The choices given are:

a. 86,400

b. 345,600

c. 691,200

d. 1,036,800

e. 2,764,800

8. A gene for sweat gland production is found on the X chromosome. If a man who lacks sweat glands marries a woman who has normal sweat glands, what will be the phenotype of their children?

A. All of the boys will lack sweat glands.

B. All of the girls will lack sweat glands.

C. The girls will have sweat glands in some areas, but lack sweat glands in others.

D. All of the boys will have sweat glands.

E. All the boys will have sweat glands, and the girls will have sweat glands in some areas but not others.

The answer is E but I'd like to know why.

If you wanted to calculate a 90% confidence interval for the difference in average
number of friendship contacts between primary aged boys and girls and we are
pretending that df=12, what t scores would you use? (assuming equal variances again)
A. ☐+/- 1.356
B. ☐+/- 2.681
C. ☐+/- 1.782
D. ☐+/- 2.179
E. ☐+/- 3.055
9. Suppose you calculated your 90% interval as described above and your lower
confidence limit was
–2.75 and your upper confidence limit was 3.20. What would that mean?
A. ☐It would mean that boys have 2.75 fewer contacts than girls on average
B. ☐It means that girls have 8.95 more contacts on average than boys
C. ☐It means that there may be no difference between the average number of
contacts for boys and girls
D. ☐It means that girls definitely have more contacts than boys
E. ☐It means that girls have 3.20 times more friendship contacts than boys
10. If you were to increase your confidence level to 99%, holding everything else
constant
A. ☐Your interval would be more precise
B. ☐You would be less likely to miss the population value
C. ☐Your interval would be wider
D. ☐You would have less confidence
E. ☐You would have to change your df

1. In families with four children, you’re interested in the probabilities for the different possible numbers of girls in a family. Using theoretical probability (assume girls and boys are equally likely), compile a five-column table with the headings “0” through “4,” for the five possible numbers of girl children in a four-child family. Then, using “G” for girls and “B” for boys, list under each heading the various birth-order ways of achieving that number of girls in a family.

Then, use your table to calculate the following probabilities:

a. The probability of 1 girl
b. The probability of 2 girls
c. The probability of 4 girls
d. The probability the third child born is a girl