You are asked to investigate the impact of diabetes on elementary school students’ academic performance. You decide to test whether the mean standardized test performance of students with diabetes is worse than the test performance of the school as a whole. The school has 235 students and the average test score for the school is set at 100 and has a standard deviation of 25. You are given data from 10 diabetic students who have an average score of 80. Please use a significance of 0.01.

a. Identify the assumed sample distribution, the formula for the test statistic, the significance level, the test distribution, and the null & alternative hypotheses

b. Calculate and report the test statistic, the input values for the test statistic, and the p value that results from the test. Also calculate the statistical power.

c. Decide whether you will reject or fail to reject the null hypothesis. Interpret that decision in the context of the problem. Evaluate the statistical power.

According to the website www.collegedrinkingprevention.gov, “About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall.” A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 99% confidence interval. He surveys a random sample of 55 students. The sample mean is 3.69 alcoholic drinks per week. The sample standard deviation is 3.56 drinks.

Construct the 99% confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college.

( ,  )

Your answer should be rounded to 2 decimal places.

Question 5

Estimating Mean SAT Math Score

The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let’s assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year. The researcher chooses a random sample of 695 exams in his state. The sample mean for the test is 487.

Find the 90% confidence interval to estimate the mean SAT math score in this state for this year.

(Note: The critical z-value to use, zc, is: 1.645.)

( , )

Your answer should be rounded to 3 decimal places.

Question 6

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 128 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 257 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length.

Find the 95% confidence interval to estimate the length of pregnancy for women who smoke.

(Note: The critical z-value to use, zc, is: 1.960)

( , )

Your answer should be rounded to 3 decimal places.

7) A researcher suspects that there is a direct relationship between hand-eye coordination and academic success in math. A sample of n = 16 students who have demonstrated above average performance on a second-grade math test is selected. These students are given a standardized hand-eye coordination task where the average score for this group is μ = 55. The 16 students in the sample produced a mean of 61 with SS of 540.

     a) Are the data sufficient to conclude that the high math achievement students have hand-eye

          coordination scores that are significantly different from the general population? Use a two-tailed

          test with α = .01.

     b) Are the data sufficient to conclude that the high math achievement students have hand-eye

          coordination scores that are significantly better than the general population? Use a one-tailed  

          test with α = .01.

8) A newspaper article reported that the typical American family spent an average of μ = $81 for Halloween candy and costumes last year. A sample of n =16 families this year produced a mean of $85 with SS = 6000. Do these data indicate a significant change in holiday spending? Use a two tailed test with α = .05.

Recently, a large academic medical center determined that

99

of

2020

employees in a particular position were

malemale​,

whereas

4242​%

of the employees for this position in the general workforce were

malemale.

At the

0.050.05

level of​ significance, is there evidence that the proportion of

malemales

in this position at this medical center is different from what would be expected in the general​ workforce?

What are the correct hypotheses to test to determine if the proportion is​ different?

A.

H0​:

piπnot equals≠0.420.42​;

H1​:

piπequals=0.420.42

B.

H0​:

piπequals=0.420.42​;

H1​:

piπnot equals≠0.420.42

Your answer is correct.

C.

H0​:

piπgreater than or equals≥0.420.42​;

H1​:

piπless than<0.420.42

D.

H0​:

piπless than or equals≤0.420.42​;

H1​:

piπgreater than>0.420.42

Calculate the test statistic.

Upper Z Subscript STATZSTATequals=nothing

​(Type an integer or a decimal. Round to two decimal places as​ needed.)

Lary got a referral from a school to run an academic motivation program to 4th graders who got low grades in their last year. She wanted to check whether these students are below average for the intelligence level. The mean IQ of her students is 98, SD is 10, and she has 25 students. The average IQ is known as 100.

1. Indicate the null and research hypothesis.
2. What test do you do to test the null hypothesis above, among independent-sample t-test, paired-sample t-test, or one-sample t-test?
3. What is the t-statistics?
4. What is the d.f. for the test?
5. Do you reject the null hypothesis?
6. So, is the average IQ score of her class significantly different from 100?

You work as a college professor during the academic year but have the summers off. You love Salmon fishing on the Kenai River in Alaska. You decide to purchase a fishing camp for $570,000 on May 15 so you can rent the cabins out and be a fishing guide for your customers. Your appraiser tells you that the land is worth 30.00% of your purchase price. You immediately build a large pavillion to hold your daily cookouts at a cost of $17,000. You hold the property for five years and sell it for $710,000. What is your accumuated depreciation over the five-year holding period?​ (The answer is $69,964 but I don't understand how to get this answer so please show your work-answer does need to be exact) Thanks!

Recently, a large academic medical center determined that 10 of 24 employees in a particular position were male​, whereas 44​% of the employees for this position in the general workforce were male. At the 0.05 level of​ significance, is there evidence that the proportion of males in this position at this medical center is different from what would be expected in the general​ workforce?

What are the correct hypotheses to test to determine

Calculate the test statistic.

Identify the​ p-value from your technology​ output, rounding to three decimal places.