Use the following data to: draw a scatter plot, find the coefficient correlation, find the regression line, predict y' for x =90.

First Test - X Final test Y

73 70

86 80

93 96

92 85

72 68

65 68

58 62

75 78

Assume that IQ scores for a certain population are approximately normally distributed. TotestH0 :μ=110againstH1 :μ̸=110,wetakearandomsampleofsizen=16from this population and observe x ̄ = 113.5 and s = 10. Do the test with significance level α = 0.05.

(a) Find the test statistic.
(b) Find the critical value from the t-table. (c) Do we accept or reject H0?

(d) Construct the confidence interval related to the test. What is your decision based on the confidence interval?

According to data from the Tobacco Institute Testing Laboratory, a certain brand of cigarette contains an average of 1.4 milligrams of nicotine. An advocacy group questions this figure, and commissions an independent test to see if the the mean nicotine content is higher than the industry laboratory claims.
The test involved randomly selecting n=15n=15 cigarettes, measuring the nicotine content (in milligrams) of each cigarette. The data is given below.

1.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.51.7,1.6,1.8,2.0,1.4,1.4,1.9,1.6,1.3,1.5,1.2,1.4,1.7,1.2,1.5

(a) Do the data follow an approximately Normal distribution? Use alpha = 0.05.  ? yes no

(b) Determine the PP-value for this Normality test, to three decimal places.
P=P=

(c) Choose the correct statistical hypotheses.
A. H0:X¯¯¯¯>1.4,HA:X¯¯¯¯<1.4H0:X¯>1.4,HA:X¯<1.4
B. H0:X¯¯¯¯=1.4,HA:X¯¯¯¯<1.4H0:X¯=1.4,HA:X¯<1.4
C. H0:μ>1.4,HA:μ<1.4H0:μ>1.4,HA:μ<1.4
D. H0:μ=1.4HA:μ>1.4H0:μ=1.4HA:μ>1.4
E. H0:μ=1.4,HA:μ≠1.4H0:μ=1.4,HA:μ≠1.4
F. H0:X¯¯¯¯=1.4,HA:X¯¯¯¯≠1.4H0:X¯=1.4,HA:X¯≠1.4


(d) Determine the value of the test statistic for this test, use two decimals in your answer.
Test Statistic =

(e Determine the PP-value for this test, to three decimal places.
P=P=

(f) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use alpha = 0.05

Ocean currents are important in the studies of climate change as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, new guinea, and other islands. X represent the number of days to recovery of a drift bottle after release and why represent the distance from point of release to point of recovery in km/100. The following data are taken from the reference by professor E.A. Kay, University of Hawaii.

x days 74 79 34 97 208

y km/100 14.6 19.5 5.3 11.6 35.7

Test slope in regression use significance level of 0.05

Find a confidence interval

Let X1, X2, X3, X4 denote 4 independent observations from a distribution with density f(x;theta)=(1+theta)x^theta, if 0<=x<=1; 0 Otherwise.. What is the form of the LRT critical regoon for testing H0:theta =2 versus H1:theta=5

ANSWER ALL PARTS USE A TI84. All other methods give the wrong answer

The following is a chart of 25 baseball players' salaries and statistics from 2016.

In order to have correlation with 95% confidence (5% significance), what is the critical r-value that we would like to have?  

(Round to three decimal places for all answers on this assignment.)

RBI vs. Salary

Complete a correlation analysis, using RBI's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No

HR vs. Salary

Complete a correlation analysis, using HR's as the x-value and salary as the y-value.

Correlation coefficient:

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No   

AVG vs. Salary

Complete a correlation analysis, using AVG as the x-value and salary as the y-value.

Correlation coefficient:   

Regression Equation: y=

Do you have significant correlation? Select an answer Yes No

Prediction

Based on your analysis, if you had to predict a player's salary, which method would be the best? Select an answer Regression equation with RBI's Regression equation with HR's Regression equation with AVG The average of the 25 salaries

Using that method, predict the salary for Mike Trout. His stats were:

RBI: 100

HR: 29

AVG: 0.315

Based on your analysis, his predicted salary would be: $_____________ million  

His actual salary was $16.083 million.

2.3) A starting lineup in basketball consists of two guards, two forwards, and a center.

(a) A certain college team has on its roster four centers, four guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.]

(b) Now suppose the roster has 4 guards, 5 forwards, 4 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 15 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)

At wind speed above 1000 cm/sec, significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand, and wind speeds above 1000 cm/sec move sand to new locations. The cycling nature of wind and moving sand determines the shape and location of large sand dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty wind speed readings gave an average velocity of 1075cm/sec. Based on long-term experience, σ can be assumed to be 265 cm/sec.

a) Calculate and interpret a 95% confidence interval for the true population mean wind speed at this site.

b) Obtain the interval using Excel and show your output.

c) Does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site? Explain.

d) In order to trust the information in the interval, is there anything else about these data that we need to know?

e) What is the margin of error for this interval? Show calculation.

f) If we want to reduce the margin of error to 40 cm/sec, how big must the sample size be?

The coefficient of determination, R2 : Is always negative May be negative or positive Ranges from -1 to +1 Ranges from zero to one Is the ratio of unexplained variation to explained variation Is the ratio of explained variation to unexplained variation has the same sign as the slope of the regression line

In a 1985 study of the relationship between contraceptive use and infertility, 89 of 283 infertile women, compared to 640 of 3833 control (fertile) women, had used an intrauterine device (IUD) at some point in their life. Use the contingency table to test for significant differences in contraceptive use patterns between the two groups. Compute a 95% CI for the difference in the proportion of women who have ever used IUDs between the infertile and fertile women. Compute the OR in favor of ever using an IUD for fertile vs. infertile women. Provide a 95% CI for the true OR corresponding to your answer. What is the relationship between your answers to questions 1 and 4? Need help with question 3 and 4

The scores on a standardized test have an average of 1200 with a standard deviation of 60. A sample of 50 scores is selected.

What is the probability that the sample mean will be between 1195 and 1205? Round your answer to three decimal places.

5. Random pigeonholing

100 pigeons p1,…,p100 fly into 500 labelled holes h1,…,h500. Each pigeon picks a hole uniformly at random and independently from the choices of the other pigeons.

1. What is the probability that at least one hole contains at least 2 pigeons.
   Hint: The answer is approximately 0.9999758457295991
2. What is the probability that at least one hole contains at least 3 pigeons.
   Hint: The answer is approximately 0.4361298523736379.

The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the probability that the sample mean will be:

A.) Between 1.99 and 2.0 liters

B.) Below 1.98 liters

C.) Greater than 2.01 liters

D.) The probability is 99% that the sample mean amount of soft drink will be at least how much?

E.) The probability is 99% that the sample mean amount of soft drink will be between which two amounts?

1. According to an educational report, the amount of time that students spend “off-task” (such as by checking their phones) during a one-hour lecture is approximately normally distributed with a mean of 3.2 minutes and a standard deviation of 2.7 minutes. An educator is interested in determining at the α = 0.05 level if the average amount of time his students spend on their phones while he is lecturing differs from the value given in the journal. During a particular class period in which he has 37 students, he noted that the average amount of time students spent on their phones was 4.2 minutes.

(a) State the null and alternative hypotheses for this test.

(b) Compute an appropriate test statistic.

(c) Determine the p-value for this test.

(d) State, in words, your conclusion.

2. Construct a 95% confidence interval for the mean amount of time students spend on their phones. Does this confidence interval support your conclusion from the hypothesis test in part (d)? Why or why not?

Consider a population having a standard deviation equal to 9.94. We wish to estimate the mean of this population.

(a) How large a random sample is needed to construct a 95% confidence interval for the mean of this population with a margin of error equal to 1? (Round your answer to the next whole number.)

The random sample is __________ units.

(b) Suppose that we now take a random sample of the size we have determined in part a. If we obtain a sample mean equal to 345, calculate the 95% confidence interval for the population mean. What is the interval’s margin of error? (Round your answers to the nearest whole number.)

The 95% confidence interval is            [ , ] .

Margin of error = ____________