Do 9-year-old boys and girls have different average height? Please answer the question by performing an appropriate hypothesis test at the 10% significance level based on the sample results below:

Boys: n1= 60, 1x=123, S1= 10

Girls: n2= 50, 1x=126, S2= 1

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You collect data to answer the research question, “Are high school boys involved in more automobile accidents than high school girls?” After conducting a hypothesis test, you conclude that there is sufficient evidence to reject the null hypothesis at α = 0.05. Use complete sentences to answer the following.

1. What were your null and alternative hypotheses in words?
   
2. State your conclusion pertaining to real-life in words.
   
3. If this conclusion is actually NOT correct, what type of error is this? State the correct conclusion in words.
   
4. What are some possible consequences of this error?
   
5. How might you change the alpha level to reduce this type of error? Explain.

A random sample of 80 baby boys, show they weighed 3000 grams on average with a standard deviation of 100, at birth. While a random sample of 60 baby girls show they weighed 2800 grams on average with a standard deviation of 70. In order to test the hypothesis that if baby boys and girls weights have the same variance or not, what is the value of test statistic?

A) 2.041

B) 0.490

C) 0.7

D) 1.429

According to U.S census estimates there were about 20 million children between 8 and 12 years old( referred to as tweens) in the united states in 2009. A recent survey of 1, 223 8- to 12 -year-old children ( S. Jayson , it's cooler than ever to be a tween.''USA today February 4, 2009 pp, 1A, 2A) reported the following results, Suppose that the survey was based on 600 boys and 623 girls.

What tween did in the past week Boys girls

Played a game on a video 498 243

Game system

Read a book for fun 276 324

Gave product advice to parents 186 181

Shopped a mall 144 262

For each type of activity, determine whether there is a difference between boys and girls at the 0.05 level of significance.

A study claims that girls and boys do not do equally well on math tests taken from the 2nd to 11th grades (Chicago Tribune, July 25, 2008). Suppose in a representative sample, 344 of 430 girls and 369 of 450 boys score at proficient or advanced levels on a standardized math test. (You may find it useful to reference the appropriate table: z table or t table)

Let p₁ represent the population proportion of girls and p₂ the population proportion of boys.

a. Construct the 95% confidence interval for the difference between the population proportions of girls and boys who score at proficient or advanced levels. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

b. Select the appropriate null and alternative hypotheses to test whether the proportion of girls who score at proficient or advanced levels differs from the proportion of boys.

• H₀: p₁ − p₂ = 0; H_A: p₁ − p₂ ≠ 0

• H₀: p₁ − p₂ ≤ 0; H_A: p₁ − p₂ > 0

• H₀: p₁ − p₂ ≥ 0; H_A: p₁ − p₂ < 0

c. At the 5% significance level, what is the conclusion to the test? Do the results support the study’s claim?

• Reject H₀; the study's claim is supported by the sample data.

• Reject H₀; the study's claim is not supported by the sample data.

• Do not reject H₀; the study's claim is supported by the sample data.

• Do not reject H₀; the study's claim is not supported by the sample data.

A snooker club can be used by players of both sex i.e. male and female, but not both at the same time. If a boy is in the club, other boys may enter, but any girl wishing to play snooker should wait until all boys leave and club become empty. Similarly, if a girl is in the club, other girls may enter, but any boy wishing to play should wait till the club becomes empty. Implement a solution to this problem using SEMAPHORES. At maximum only 6 boys or 6 girls can enter the club and play snooker as there are only 3 tables available in the club.

You wish to see if there is a difference between the average score of boys and girls on the math SOL. A random sample of 195 boys had an average score of 444.34 with a standard deviation of 45.65. A random sample of 202 girls had an average score of 452.64 and a standard deviation of 37.75.

A: Verify the assumptions.

B: State the 95% confidence interval for the difference of the average SOL scores.

C: Does this interval shows, at 95% confidence, that the averages are different.

You wish to see if there is a difference between the average score of boys and girls on the math SOL. A random sample of 195 boys had an average score of 444.34 with a standard deviation of 45.65. A random sample of 202 girls had an average score of 452.64 and a standard deviation of 37.75.

A: Verify the assumptions.

B: State the 95% confidence interval for the difference of the average SOL scores.

C: Does this interval shows, at 95% confidence, that the averages are different.