Arden and Plomin (2006) published a study reporting that IQ scores for boys are more variable than IQ scores for girls. A researcher would like to know whether this same phenomenon applies to other measures of cognitive ability. A standard cognitive skills test is given to a sample of n = 15 adolescent boys and a sample of n = 15 adolescent girls, and resulted in the following scores. Boys Girls 9 5 3 9 7 6 5 4 6 7 5 2 4 8 8 6 4 7 6 8 7 4 9 7 3 5 7 8 6 5 1) Calculate the mean and the standard deviation for each group. Boys: Girls: 2) Based on the means and the standard deviations, describe the differences in intelligence scores for boys and girls. A- The girl's mean intelligence score is HIGHER THAN, LOWER THAN, OR THE SAME AS that the boy's scores. B- The boys’ scores are AS VARIABLE AS, LESS VARIABLE THAN, OR MORE VARIABLE THAN the girls’ scores?

Body mass index (BMI) is a reliable indicator of body fat for most children and teens. BMI is calculated from a child’s weight and height and is used as an easy-to-perform method of screening for weight categories that may lead to health problems. For children and teens, BMI is age- and sex-specific and is often referred to as BMI-for-age.

The Centers for Disease Control and Prevention (CDC) reports BMI-for-age growth charts for girls as well as boys to obtain a percentile ranking. Percentiles are the most commonly used indicator to assess the size and growth patterns of individual children in the United States.

The following table provides weight status categories and the corresponding percentiles and BMI ranges for 10-year-old boys in the United States.Page 241

Health officials of a Midwestern town are concerned about the weight of children in their town. They believe that the BMI of their 10-year-old boys is normally distributed with mean 19.2 and standard deviation 2.6.

In a report, use the sample information to

1. Compute the proportion of 10-year-old boys in this town that are in the various weight status categories given the BMI ranges.

2. Discuss whether the concern of health officials is justified.

2. On average, do males start smoking at an earlier grade than females? Data from 94 12th grade boys that smoke and 108 12th grade females that smoke found that the mean grade of first use of cigarettes was 9.87 for boys (standard deviation of 1.75), and 10.17 for girls (standard deviation of 1.69).

a) Is this sufficient evidence at alpha =.05 that the mean grade for first-time cigarette use is lower for boys than for girls? (10 points)
b) Calculate and interpret a 99.9% confidence interval for the mean difference between all boys and girls in the mean grade of first cigarette use. (6 points)

c) What is the margin of error for the confidence interval you calculate in part B? (2 points)

d) Based on the confidence interval you calculated in part B, we are 99.9% confident (1 point)
i. That the mean grade for first-time cigarette use is lower for boys than for girls.
ii. That the mean grade for first-time cigarette use is higher for boys than for girls.
iii. That it is plausible that there is no difference in the mean grade for first-time cigarette use between boys and girls.

iv. We can’t conclude anything at alpha=.001 based on this confidence interval.
e) Calculate and interpret a 95% confidence interval for the mean grade of first use of cigarettes for boys. (6 points)

In a recent survey of 200 elementary students, many revealed they preferred math than English. Suppose that 80 of the students surveyed were girls and that 120 of them were boys. In the survey, 60 of the girls, and 80 of the boys said that they preferred math more.

1. What is the difference in the probability between that girls prefer math more and boys prefer math more?

a.0.0833

b. 0.5

c 0.0042

d. 0.4097

2. What is the standard error of the difference in the probability between that girls prefer math more and boys prefer math more?

a.0.4097

b.0.0042

c. 0.0833

d. 0.0647734

3. Calculate an 80% confidence interval for the difference in proportions

4. Suppose the 90% confidence interval for the difference in proportion is (-0.0232, 0.1899).

Is the following interpretation of the confidence interval true?

"For all elementary students, I have 90% confidence that the true proportion difference between girls and boys is in the interval (-0.0232, 0.1899)."

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, 994 births consisted of 521 baby girls and 473 baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 521 girls in 994 births.

b. Find the probability of getting 521 or more girls in 994 births. If boys and girls are equally​ likely, is 521 girls in 994 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?

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, 860 births consisted of 433 baby girls and 427 baby boys. In analyzing these​ results, assume that boys and girls are equally likely. a. Find the probability of getting exactly 433 girls in 860 births. b. Find the probability of getting 433 or more girls in 860 births. If boys and girls are equally​ likely, is 433 girls in 860 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?

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, 803 births consisted of 420 baby girls and 383 baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 420 girls in 803 births.

b. Find the probability of getting 420 or more girls in 803 births. If boys and girls are equally​ likely, is 420 girls in 803 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?

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, 964 births consisted of 504 baby girls and 460 baby boys. In analyzing these results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 504 girls in 964 births.

b. Find the probability of getting 504 or more girls in 964 births. If boys and girls are equally likely, is 504 girls in 964 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?

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,

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births consisted of

448448

baby girls and

414414

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

a. Find the probability of getting exactly

448448

girls in

862862

births.

b. Find the probability of getting

448448

or more girls in

862862

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

448448

girls in

862862

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?