2. A business school curriculum committee is evaluating three formats for lab sections to accompany a traditional class. A standard examination generated the following average scores for some sample classes.

                                                                 Lab Method

                               Lecture                     Computer                   Mixed

                                    78                                77                                83

                                    85                                86                                91

                                    64                                71                                75                   

                                    77                                75                                78

                                    81                                80                                82

                                    75                                77                                80

test to see if there is a difference in the average scores across the different methods. Use alpha = 0.05.

9.
A school social worker wants to determine if the grade distribution of home-schooled children is different in her
district than nationally. A national statistical center provided her with the data in the first table below, which
represent the relative frequency of home-schooled children by grade level. She obtains a sample of
home-schooled children within her district that yields the data in the second table below.
Grade Relative Frequency Grade Frequency
K 0.045 K 4
1-3 0.256 1-3 9
4-5 0.122 4-5 2
6-8 0.274 6-8 6
9-12 0.303 9-12 4

(a) Because of the low cell counts, combine cells into three categories K-3, 4-8, and 9-12.
Grade Relative Frequency Observed Frequency Expected Frequency
K-3 ? ? ?
4-8 ? ? ?
9-12 ? ? ?
(Type integers or decimals rounded to three decimal places as needed.)

(b) Is the grade distribution of home-schooled children different in her district from the national grade distribution
at the α = 0.01 level of significance?

What are the hypotheses?
(1) H₀ or H₁ : The grade distribution of home-schooled children in her district is the national
grade distribution of home-schooled children.

(2) H₀ or H₁ : The grade distribution of home-schooled children in her district is the national
grade distribution of home-schooled children.

Use technology to compute the P-value for this test at α = 0.01 level of significance.
P-value = (Round to three decimal places as needed.)

Find the conclusion to the hypothesis test.
(3) reject / do not reject the null hypothesis.

There (4) is / is not sufficient evidence at the level of
significance to conclude that the grade distribution of home-schooled children in her district is (5) the same as / different from
the national grade distribution of home-schooled children.

Lionel is an unmarried law student at State University Law School, a qualified educational institution. This year Lionel borrowed $24,000 from County Bank and paid interest of $1,840. Lionel used the loan proceeds to pay his law school tuition. Calculate the amount Lionel can deduct for interest on higher education loans. Lionel’s AGI before deducting interest on higher education loans is $82,000.

Tim is a single, cash-method taxpayer with an AGI of $50,000. In April of this year Tim paid $1,020 with his state income tax return for the previous year. During the year, Tim had $5,400 of state income tax and $18,250 of federal income tax withheld from his salary. In addition, Tim made estimated payments of $1,160 and $1,900 of state and federal income taxes, respectively. Finally, Tim expects to receive a refund of $500 for state income taxes when he files his state tax return for this year in April next year. What is the amount of taxes that Tim can deduct as an itemized deduction?

This year Randy paid $29,000 of interest (Randy borrowed $450,000 to buy his residence, and it is currently worth $500,000). Randy also paid $2,500 of interest on his car loan and $4,200 of margin interest to his stockbroker (investment interest expense). Randy received $2,600 of interest this year and no other investment income or expenses. His AGI is $75,000. How much of this interest expense can Randy deduct as an itemized deduction?

A high school believes that their seniors have gotten exceptionally high SAT scores this year, and they want to compare the SAT scores of their 400 seniors to the SAT scores of all the high school seniors in the country.  

What is the best statistical test to use to analyze the hypothesis in scenario 1?

Group of answer choices

One-way ANOVA

Two Sample Z-Test

Factor Analysis

Correlation Coefficient

Independent sample t-Test

Dependent sample t-Test

Z-Score

Structural Equation Model

One Sample Z-Test

Which of the following is the null hypothesis for scenario 1?

Group of answer choices

HO: µ1 = µ2

HO: µ1 = µ2 =µ3

H0: X = µ

r = 0

What is the alternative hypothesis for scenario 1?

Group of answer choices

H1: X1 ≠ X2 ≠ X3

H1: X ≠ µ

r ≠ 0

H1: m1 < m2

Researchers are interested in studying whether time spent on social media is associated with happiness. They ask participants to rate the amount of time they spend on social media each week, and also measures their reports of happiness (on a scale of 1-10).

Which of the following is the null hypothesis for scenario 2?

Group of answer choices

H0: X = µ

H0: rxy > 0

H0: µ1 = µ2 = µ3

H0: rxy = 0

Which of the following is the alternative hypothesis for scenario 2?

Group of answer choices

H₁: rxy = 0

H₁: rxy >0

H₁: X ≠ µ

H₁: µ1 ≠ µ2 ≠µ3

Which of the following is the independent variable for scenario 2?

Group of answer choices

There is no independent variable in this study (because it is correlational)

Time spent on social media

Happiness

The participants

The laboratory

Which of the following is the dependent variable for scenario 2?

Group of answer choices

The participants

There is no dependent variable in this study (because it is correlational)

Time spent on social media

Happiness

The laboratory

W

hat is the best statistical test to use to analyze the hypothesis in scenario 2?

Group of answer choices

Dependent sample t-Test

z-test

Independent sample t-Test

Structural Equation Model

Correlation Coefficient

z-score

One-way ANOVA

Factor Analysis

Many high school students take the AP tests in different subject areas. In 2007, of the 143044 students who took the AP biology exam 76712 of them were female. In that same year, of the 211993 students who took the AP calculus AB exam 100106 of them were female. Is there enough evidence to show that the proportion of AP biology exam takers who are female is higher than the proportion of AP calculus AB exam takers who are female?

a) Test at the 5% level

b) Compute a 90% confidence interval for the difference in proportions.

Use the steps of PHANTOMS for the hypothesis test.

For the confidence interval you do not need to do all the steps of PANIC since you did some of them already in PHANTOMS.

You just need to do the NIC of PANIC.

Part a.) HYPOTHESIS TEST

P: Parameter

What is the correct parameter symbol and wording for population 1?

     Select an answer p̂₁ N₁ n₁ p₁ μ? X̄ μ₁  = Select an answer A randomly selected student who took the AP biology test that is female The percentage of all students who took the AP biology test that are female A randomly selected student who took the AP biology test 143044 randomly selected students who took the AP biology test All students who took the AP biology test The percentage of 143044 randomly selected students who took the AP biology test that are female All students who took the AP biology test that are female Whether or not a randomly selected student who took the AP biology test is female

     What is the correct parameter symbol and wording for population 2?

     Select an answer μ? p̂₂ N₂ μ₂ p₂ X̄₂ n₂  = Select an answer All students who took the AP calculus AB test that are female The percentage of all students who took the AP calculus AB test that are female All students who took the AP calculus AB test A randomly selected student who took the AP calculus AB test The percentage of 211993 randomly selected students who took the AP calculus AB test that are female A randomly selected student who took the AP calculus AB test that is female Whether or not a randomly selected student who took the AP calculus AB test is female 211993 randomly selected students who took the AP calculus AB test

H: Hypotheses

Fill in the correct null and alternative hypotheses:

H0:H0: Select an answer μ₁ - μ₂ p₁ - p₂ X̄₁ - X̄₂ N₁ - N₂ p̂₁ - p̂₂ n₁ - n₂ μ?  ? > ≥ = ≠ ≤ <  

HA:HA: Select an answer μ₁ - μ₂ n₁ - n₂ X̄₁ - X̄₂ p̂₁ - p̂₂ N₁ - N₂ p₁ - p₂ μ?  ? ≠ ≥ = > < ≤  

A: Assumptions

Since Select an answer quantitative qualitative  information was collected from each object, we need to check the following conditions:

Check all that apply.

    

• Normal population or at least 30 pairs of data with no outliers in the differences
• σσ is unknown for each group.
• The samples are dependent.
• n1−x1≥10n1-x1≥10 and n2−x2≥10n2-x2≥10
• The samples are independent.
• x1≥10x1≥10 and x2≥10x2≥10
• Normal population or n1≥30n1≥30 and n2≥30n2≥30 with no outliers for each group.
• N1≥20n1N1≥20n1 and N2≥20n2N2≥20n2

     Check those assumptions:

x1x1 =  which is ? ≥ ≠ = < > ≤  

x2x2 =  which is ? > ≥ < ≤ = ≠  

n1−x1n1-x1 =  which is ? ≥ = < ≠ > ≤  

n2−x2n2-x2 =  which is ? = ≤ > < ≠ ≥  

Population sizes are not given.

We will assume that N1N1 >= 20(n1)n1) and N2N2 >= 20(n2)n2)

N: Name the test

The conditions are met to use a Select an answer T-Test Paired T-Test 2-Proportion Z-Test 2-Sample T-Test 1-Proportion Z-Test  .

T: Test Statistic

The symbol and value of the random variable (to 4 decimal places) on this problem are as follows:

     Select an answer n₁ - n₂ N₁ - N₂ μ₁ - μ₂ p₁ - p₂ μ? p̂₁ - p̂₂ X̄₁ - X̄₂  =

Pooled Sample proportion of ˆpp^ is as follows:

     (Leave your answer in FRACTION form and use this fraction form in the set up of the test statistic)

ˆpp^ = x1+x2n1+n2x1+x2n1+n2 =

(( ++  )) /(/(  ++  )=)=

Set up the formula for the test statistic with EXACT FRACTIONS or given decimal values for each box:
z=ˆp1−ˆp2√ˆp(1−ˆp)(1n1+1n2)=z=p^1-p^2p^(1-p^)(1n1+1n2)=

((  −-  ) / √(( ⋅⋅ (1−(1- )⋅ (1)⋅ (1/  +1+1/  ))=))=

Round final answer from technology to 2 decimal places.

     z =

O: Obtain the P-value

Report the final answer to 4 decimal places. It is possible when rounded that a p-value is 0.0000

     P-value =

M: Make a decision

Since the p-value ? = ≤ ≠ ≥ < >   , we Select an answer accept H₀ reject Hₐ fail to reject H₀ fail to reject Hₐ reject H₀  .

S: State a conclusion

• There Select an answer is not is  significant evidence to conclude Select an answer All students who took the AP biology test that are female Whether or not a randomly selected student who took the AP biology test is female 143044 randomly selected students who took the AP biology test The percentage of all students who took the AP biology test that are female A randomly selected student who took the AP biology test The percentage of 143044 randomly selected students who took the AP biology test that are female All students who took the AP biology test A randomly selected student who took the AP biology test that is female  Select an answer is more than is less than is equal to differs from  Select an answer 211993 randomly selected students who took the AP calculus AB test The percentage of all students who took the AP calculus AB test that are female The percentage of 211993 randomly selected students who took the AP calculus AB test that are female All students who took the AP calculus AB test that are female A randomly selected student who took the AP calculus AB test Whether or not a randomly selected student who took the AP calculus AB test is female All students who took the AP calculus AB test A randomly selected student who took the AP calculus AB test that is female
  

Part b.) CONFIDENCE INTERVAL

N: Name the procedure

   The conditions are met to use a Select an answer Paired T-Interval 2-Sample T-Interval T-Interval 2-Proportion Z-Interval 1-Proportion Z-Interval

I: Interval estimate (round endpoints to 3 decimal places)

A  % confidence interval for Select an answer p₁ - p₂ μ? μ₁ - μ₂ n₁ - n₂ X̄₁ - X̄₂ p̂₁ - p̂₂ N₁ - N₂  is (  ,   )

C: Conclusion in context

• We are  % confident that Select an answer All students who took the AP biology test that are female Whether or not a randomly selected student who took the AP biology test is female 143044 randomly selected students who took the AP biology test All students who took the AP biology test The percentage of 143044 randomly selected students who took the AP biology test that are female A randomly selected student who took the AP biology test A randomly selected student who took the AP biology test that is female The percentage of all students who took the AP biology test that are female  is between  % and  % Select an answer more than less than  Select an answer A randomly selected student who took the AP calculus AB test that is female Whether or not a randomly selected student who took the AP calculus AB test is female All students who took the AP calculus AB test that are female All students who took the AP calculus AB test The percentage of all students who took the AP calculus AB test that are female A randomly selected student who took the AP calculus AB test 211993 randomly selected students who took the AP calculus AB test The percentage of 211993 randomly selected students who took the AP calculus AB test that are female

LicensePoints possible: 58
This is attempt 1 of 2.

A high school psychologist was concerned about the equivalency of two types of standardized tests given to students as part of their college entrance exams. She set out to see if there was a positive correlation between the two exams. She sampled 5 students who took both exams. Use the data below to answer questions 10-14:

Subject                Test A                   Test B

1                          700                         35

2                          772                         38

3                          605                         36

4                          721                         39

5                          695                         34

10. What is the correlation coefficient?
11. How many tails does the test have?
12. What are the degrees of freedom?
13. What is the critical r value for a level of significance of 0.01?
14. What do you conclude about the data?

Data collected from a local high school found that 18% of the students do not have internet access at home, which puts these students at a disadvantage academically. One teacher felt this estimate was too low and decided to test if the true percentage of students without home internet access was greater than the data suggested. To do this, she sampled 200 students. In her sample, 25% of the students did not have internet access at home. If the significance level for the hypothesis test is 1%, can the teacher conclude that more than 18% of all such students do not have internet access?

When answering the questions below

• make sure a decimal representation begins with 0, like this: 0.286
• if a test has two Critical Values, type it like this: -2.34 & 2.34
• round z values to 2 decimal places, and t values to 3 decimal places
• for the result, type either Reject, or Fail to Reject

Please type in the Critical Value(s) , the Test Statistic , and the result of the test

Emily, who was active in sports throughout high school, has decided to run a marathon with some of her friends. She is 27 years old, 5 ft 7 in tall, and weighs 125 pounds. She eats all kinds of foods, likes fruits and vegetables, but tries to avoid fatty foods. She says coffee is her downfall—she drinks 6 cups a day. She doesn’t like sweets, although she keeps ice cream in her freezer. A family history notes that her mother   had a   stroke shortly after menopause and that her father is not at risk for any chronic conditions. Although she would eventually like to have children, Kristen is not pregnant now.

Make three suggestions that could improve Emily’s diet.

A survey of high school students revealed that the numbers of soft drinks consumed per month was normally distributed with mean 25 and standard deviation 15. A sample of 36 students was selected. What is the probability that the average number of soft drinks consumed per month for the sample was between 26.2 and 30 soft drinks?

Write only a number as your answer. Round to 4 decimal places (for example 0.0048). Do not write as a percentage.