We wish to compare the prevalence of parasites in Mediterranean fish to the prevalence of parasites in Atlantic fish. In the Mediterranean Sea 500 brill were captured and dissected; 150 were found to contain parasites   In the Atlantic 200 brill were captured and dissected; 40 were found to have parasites. In what follows, let p₁ denotes the infestation rate for the Mediterranean brill and p₂ denote the infestation rate for the Atlantic brill. Find the margin of error for the 90% confidence interval for the difference p₁   - p_2..

0.12

0.07

0.04

0.06

0

Researchers would like to know whether the proportions of elementary school children who are obese differ in rural and urban area. An earlier study found that 50% of urban school children and 45% of rural school children are obese. The researchers select 153 urban school children and 191 rural school children. Suppose [^(p)]₁ and [^(p)]₂ denote sample proportions of urban and rural school children respectively who are obese.
Answer all the questions below (where appropriate) as a fraction not as a percentage.

What is the expected proportion of obese among urban school children, i.e. expected value of [^(p)]₁? [Answer to two decimal places.]

What is the standard deviation of proportion of obese among urban school children, i.e. σ([^(p)]₁)? [Answer to four decimal places.]

What is the expected proportion of obese among rural school children, i.e. expected value of [^(p)]₂? [Answer to two decimal places.]

What is the standard deviation of proportion of obese among rural school children, i.e. σ([^(p)]₂)? [Answer to four decimal places.]

What is the expected difference of proportions of obese between urban and rural school children, i.e. expected value of [^(p)]₁ − [^(p)]₂? [Answer to two decimal places.]

What is the standard deviation of difference of proportions of obese between urban and rural school children, i.e. σ([^(p)]₁ − [^(p)]₂)? [Answer to four decimal places.]

What is the probability that the difference of proportions of obese between urban and rural school children will be larger than 0.10? i.e. find P([^(p)]₁ − [^(p)]₂ > 0.10). [Answer to four decimal places.]

In the table, below, the number of correctly remembered words are listed for both tests (see #1, above). Based on these results, calculate the appropriate test for these data (assume a = .05) to determine if the memory enhancement training program produces better recall. Be sure to state the calculated and critical values of the statistic for this test. Would you reject or fail to reject the null hypothesis in this situation? Why? Show your work and include all formulas that you're using!

Student; Score 1; Score 2

1; 24 ; 26

2 ; 17; 24

3 ; 32 ; 31

4 ; 14 ; 17

5 ; 16 ; 17

6 ; 22 ; 25

7 ; 26 ; 25

8 ; 19; 24

9 ; 19 ; 22

10 ; 22; 23

11 ; 21; 26

12 ; 25; 28

13; 16 ; 19

14 ; 24 ; 23

15 ; 18 ; 22

Starting salaries of 64 college graduates who have taken a statistics course have a mean of $42,500 with a standard deviation of $6,800. Find an 90% confidence interval for ?μ. (NOTE: Do not use commas or dollar signs in your answers. Round each bound to three decimal places.)

Each bound should be rounded to three decimal places.

A random sample of ?=100 observations produced a mean of ?⎯⎯⎯=32 with a standard deviation of ?=4

(a) Find a 95% confidence interval for ?μ
Lower-bound:  

Upper-bound:

(b) Find a 90% confidence interval for ?μ
Lower-bound:  

Upper-bound:

(c) Find a 99% confidence interval for ?μ
Lower-bound:  

Upper-bound:

A simple random sample of 70 items resulted in a sample mean of 90. The population standard deviation is

σ = 5.

(a)

Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)

to

(b)

Assume that the same sample mean was obtained from a sample of 140 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)

to

(c)

What is the effect of a larger sample size on the interval estimate?

A larger sample size provides a smaller margin of error

.A larger sample size does not change the margin of error.    

A larger sample size provides a larger margin of error.

The data is presented in parallel format. Before running the ANOVA in Excel, you will need to put it into serial (column) format. You will need to create a categorical variable for the first factor (days) and for the second factor (time of day). This is a critical step.

The data presented shows exam scores for students randomly assigned to the sections meeting on these days at these times of the day:

Conduct a 2-way ANOVA. First, find the group means for each level of the factors. (Report answers accurate to 2 decimal places.)
Days:
  MThursday=
  MFriday=
Time of day:
  Mmorning=
  Mafternoon=

Report the results of the ANOVA for the main & interaction effects. (Report P-values accurate to 4 decimal places and F-ratios accurate to 3 decimal places.)
Day:
  FA=
  p=
Time of day:
  FB=
  p=
Interaction:
  FA×B=
  p=

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1249 with a standard deviation of 32 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found between and A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found between and A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found between and A.D.

You are given the following information about y and x:

Calculate the value of SSR, using the formula.

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 1400 voters in the town and found that 61 % of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is not equal to 64 % . Testing at the  0.01 level, is there enough evidence to support the strategist's claim?

State the null and alternative hypotheses.

Find the value of the test statistic. Round your answer to two decimal places.

Specify if the test is one-tailed or two-tailed.

Determine the P-value of the test statistic. Round your answer to four decimal places.

Identify the value of the level of significance.

Make the decision to reject or fail to reject the null hypothesis.

State the conclusion of the hypothesis test.

(9) A study was conducted on the amount of converted sugar in a certain process at various temperatures. The data was as follows

Temperature (x) Converted Sugar (y)

45 8.1

50 7.8

55 8.6

60 9.8

65 9.6

70 8.9

75 10.1

80 9.9

85 10.4

90 10.6

(a) Estimate the linear regression line?

(b) What is the predicted converted sugar for 95.

(c) What is the coefficient of determination? Is this a strong fit?

To test compliance with authority, a classical experiment in social psychology
requires subjects to administer increasingly painful electric shocks to seemingly
helpless victims who agonize in an adjacent room.* Each subject earns a score
between 0 and 30, depending on the point at which the subject refuses to comply
with authority—an investigator, dressed in a white lab coat, who orders the
administration of increasingly intense shocks. A score of 0 signifies the subject’s
unwillingness to comply at the very outset, and a score of 30 signifies the subject’s
willingness to comply completely with the experimenter’s orders.

Ignore the very real ethical issues raised by this type of experiment, and assume
that you want to study the effect of a “committee atmosphere” on compliance with
authority. In one condition, shocks are administered only after an affirmative decision
by the committee, consisting of one real subject and two associates of the investigator,
who act as subjects but, in fact, merely go along with the decision of the real
subject. In the other condition, shocks are administered only after an affirmative
decision by a solitary real subject.

A total of 12 subjects are randomly assigned, in equal numbers, to the committee
condition (X1) and to the solitary condition (X2). A compliance score is obtained for
each subject. Use t to test the null hypothesis at the .05 level of significance.

COMPLIANCE SCORES
COMMITTEE SOLITARY
2 3
5 8
20 7
15 10
4 14
10 0

Data from the Bureau of Labor Statistics' Consumer Expenditure Survey show customers spend an average of (µ) $608 a year for cellular phone services. The standard deviation of annual cellular spending is (σ) $132. The random variable, yearly cellular spending, is denoted by X. We plan to select a random sample of 100 cellular customers.

11.

The sampling distribution of X¯X¯

Select one:

a. is not normal because the sample size is too small

b. is normal due to the Chebyshev's Theorem

c. is normal due to the Central Limit Theorem

d. is not normal because the sample size is too large

12.

The standard error (SE) of X¯X¯ is

Select one:

a. 60.8

b. 1.32

c. 132

d. 13.2

13.

What is the probability that a random sample of 100 cellular customers will provide an average(X¯X¯) that is within $25 of the population mean (µ)?

Select one:

a. 3%

b. 94%

c. 97%

d. 6%

14.

The probability in the PRECEDING question would ------ if we were to increase the sample size (n) from 100 to 151.

Select one:

a. be zero

b. stays the same

c. increase

d. decrease

15.

Suppose we reduce the sample size (n) from 100 to 25. The sampling distribution of X¯X¯ will be normal only if

Select one:

a. X has a right skewed distribution

b. X is normally distributed

c. X has a bi-modal distribution

d. X has a left skewed distribution

Problem 6-21 (Algorithmic)

The Centers for Disease Control and Prevention Office on Smoking and Health (OSH) is the lead federal agency responsible for comprehensive tobacco prevention and control. OSH was established in 1965 to reduce the death and disease caused by tobacco use and exposure to secondhand smoke. One of the many responsibilities of the OSH is to collect data on tobacco use. The following data show the percentage of U.S. adults who were users of tobacco for a recent 11-year period (http://www.cdc.gov/tobacco/data_statistics/tables/trends/cig_smoking/index.htm).

1. e simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)
   
   y-intercept, b₀ =
   
   Slope, b₁ =
   
   MSE =
   
2. One of OSH’s goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal?
   
   
   
   Use your model from part (b) to estimate the number of years that must pass after these data have been collected before OSH will achieve this goal. Round your answer to the nearest whole number.
   
   years

1) Scientists have developed an inexpensive new test that can rapidly diagnose COVID-19 infections, a timely advance that comes as clinicians and public health officials are scrambling to cope with testing backlogs while the number of cases continues to climb. The new test – officially named the “SARS-CoV-2 DETECTR” – is easy to implement and to interpret, and requires no specialized equipment, which is likely to make the test more widely available than the current COVID-19 test kits.

To examine the effectiveness of the new COVID-19 screening test in County A. Participants were assigned to the new “SARS-CoV-2 DETECTR” screening test or the current test. The three months study period produced these results:

1. i. Calculate the sensitivity of the “SARS-CoV-2 DETECTR” screening test. (2pts)

ii. Interpret your results (0.5pt):

2. i. Calculate the specificity of the “SARS-CoV-2 DETECTR” screening test. (2pts)

ii. Interpret your results (0.5pt):

3. i. Calculate the predictive value positive of the “SARS-CoV-2 DETECTR” screening test. (2pts)

ii. Interpret your results (0.5pt):

4. i. Calculate the predictive value negative of the “SARS-CoV-2 DETECTR” screening test.. (2pts)

ii. Interpret your results (0.5pt):