A​ gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the​ gender-selection technique,

861861

births consisted of

443443

baby girls and

418418

baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly

443443

girls in

861861

births.

b. Find the probability of getting

443443

or more girls in

861861

births. If boys and girls are equally​ likely, is

443443

girls in

861861

births unusually​ high?

c. Which probability is relevant for trying to determine whether the technique is​ effective: the result from part​ (a) or the result from part​ (b)?

d. Based on the​ results, does it appear that the​ gender-selection technique is​ effective?

Wilcoxon Rank-Sum Test

Is there a difference between Girls and Boys on number of books read?

Boys 12, 5, 13, 3, 11

Girls 4, 10, 9, 7, 6

Question 1 (a): A class consists of 100 students with boys and girls’ ratios as 4:6. Find the average weight of the class if the average weight of boys and girls is 10 and 15
respectively. Also find the combined mean if the ratio of no of boys and girls is reversed.

Question 1 (b): The rice production (in Kg) of 10 acres is given as: 1120, 1240, 1320, 1040, 1080, 1720, 1600, 1470, 1750, and 1885. Find the quartile deviation and coefficient of quartile deviation.

The authors of a paper concluded that more boys than girls listen to music at high volumes. This conclusion was based on data from independent random samples of 767 boys and 750 girls from a country, age 12 to 19. Of the boys, 397 reported that they almost always listen to music at a high volume setting. Of the girls, 331 reported listening to music at a high volume setting.

Do the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls? Test the relevant hypotheses using a 0.01 significance level. (Use a statistical computer package to calculate the P-value. Use p_boys − p_girls. Round your test statistic to two decimal places and your P-value to four decimal places.)

State your conclusion.

We reject H₀. We have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

We fail to reject H₀. We have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.   

We reject H₀. We don't have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

We fail to reject H₀. We don't have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

The authors of a paper concluded that more boys than girls listen to music at high volumes. This conclusion was based on data from independent random samples of 770 boys and 748 girls from a country, age 12 to 19. Of the boys, 397 reported that they almost always listen to music at a high volume setting. Of the girls, 331 reported listening to music at a high volume setting.

Do the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls? Test the relevant hypotheses using a 0.01 significance level. (Use a statistical computer package to calculate the P-value. Use p_boys − p_girls. Round your test statistic to two decimal places and your P-value to four decimal places.)

State your conclusion.

We reject H₀. We have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

We fail to reject H₀.

We have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.    We reject H₀.

We don't have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

We fail to reject H₀. We don't have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

For decades, people have believed that boys are innately more capable than girls in math. In other words, due to the intrinsic differences in brains, boys are better suited for doing math than girls. Recent research challenges this stereotype, arguing that gender differences in math performance have more to do with culture than innate aptitude. In the U.S., for example, girls perform just as well on standardized math tests as boys. Others argue, however, that while the average may be the same, there is more variability in math ability for boys than girls, resulting in some boys with soaring math skills. A portion of representative data on math scores for boys and girls is shown in the accompanying table.

In a report, use the above information to:

1. Construct and interpret the 95% confidence interval for the ratio of the variance of math scores for boys and for girls. Discuss the assumptions made for the analysis.

2. Determine at the 5% significance level if boys have more variability in math scores than girls. (Two full sentences: one stating your decision using p-value or critical value approach and one stating your conclusion.)

Show all working out and reasoning, be specific and detailed please. Please do all working out in Excel only. Thank you. This is about Chi Squared Distribution:Statistical Inference Concerning Variance and F Distribution:Inference Concerning Ratio of Two Population Variances to give you an idea about what formulas I'm looking for. Thank you.

A report described teens' attitudes about traditional media, such as TV, movies, and newspapers. In a representative sample of American teenage girls, 42% said newspapers were boring. In a representative sample of American teenage boys, 45% said newspapers were boring. Sample sizes were not given in the report.

(a) Suppose that the percentages reported had been based on a sample of 50 girls and 60 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Use p_girls − p_boys. Round your test statistic to two decimal places and your P-value to four decimal places.)

State your conclusion.

We fail to reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We fail to reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.    

We reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

(b) Suppose that the percentages reported had been based on a sample of 2050 girls and 2800 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Use μ_girls − μ_boys. Round your test statistic to two decimal places and your P-value to four decimal places.)

State your conclusion.

We fail to reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We fail to reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.   

We reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

(c) Explain why the hypothesis tests in parts (a) and (b) resulted in different conclusions.

You are much less likely to get a difference in sample proportions as large as the one given when the samples are very large.

You are much less likely to get a difference in sample proportions as large as the one given when the number of boys vs. girls sampled are far apart.   

You are much less likely to get a difference in sample proportions as large as the one given when the number of boys vs. girls sampled are close together.

You are much less likely to get a difference in sample proportions as large as the one given when the samples are very small.

In how many ways can 2 men, 4 women, 3 boys, and 3 girls be selected from 6 men, 8 women, 4 boys and 5 girls if a particular man and woman must be selected?

Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that auto insurance rates are normally distributed for both boys and girls, and the population standard deviation for each group is  = $180. At the .01 significance level, does this data provide evidence that the mean cost for auto insurance for teenage boys is greater than that for teenage girls?

work must include

1. Clear statement of hypotheses, with the correct parameter(s)
2. An indication of the test used
3. The test statistic and p-value
4. An indication of the statistical decision (i.e. whether or not to reject Ho)
     along with an explanation.
5. An interpretation of the statistical decision in the context of the problem.  

A group of parents examines a random sample of insurance bills in order to determine if there is evidence to suggest that the cost of auto insurance for teenage boys costs more, on average, than for teenage girls. The mean annual cost for 42 teenage boys was $619. For 37 teenage girls, it was $579. From past years, it is known that the population standard deviation for each group is $150. Does this data provide evidence at a significance level of alpha equals 0.05 that the mean cost for auto insurance for teenage boys is greater than that for teenage girls?