A marine biologist claims that the mean length of mature female pink seaperch is different in fall and winter. A sample of 6 mature female pink seaperch collected in fall has a mean length of 106 millimeters and a standard deviation of 14 millimeters. A sample of 8 mature female pink seaperch collected in winter has a mean length of 101 millimeters and a standard deviation of 13 millimeters. At alphaequals 0.20​, can you support the marine​ biologist's claim? Assume the population variances are equal. Assume the samples are random and​ independent, and the populations are normally distributed.

Standardized test statistic

t = ??

A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of salespersons. Salesperson Years of Experience Annual Sales ($1000s)

1 1 80

2 2 100

3 3 106

4 4 105

5 6 111

6 8 120

7 9 121

8 11 116

9 13 136

10 14 142

The data y= on annual sales($1000s) for new customer accounts and x= number of years of experience for a sample of 10 salespersons provided the estimated regression equation y=88.22+3.59x . For these data x=7.1, (xi-x)²192.90 , and s=6.8693.

a. Develop the 95% confidence interval for the mean annual sales for all salespersons with twelve years of experience. ( , ) (to 2 decimals)

b. The company is considering hiring Tom Smart, a salesperson with twelve years of experience. Develop a 95% prediction interval of annual sales for Tom Smart. ( , ) (to 2 decimals)

a. In your own words, what is meant by the statement that correlation does not imply causality.

b.In your own words, please describe the difference between regression equation y=Bo+B1x and the regression equation ^y=bo+b1x?

Let the random variable X represent a student’s score on an IQ test. Suppose that student IQ scores are Normally distributed with a mean of 100 and a standard deviation of 15.

Part A.Any student who scores at least 130 on an IQ test would be considered gifted. If a student has scored 130 on an IQ test, what percentile does this score represent? Part B.In a class of 50 students, how many would you expect to score at least 115 on an IQ test?

Part C.Suppose that 10 students are randomly selected from a large school. What is the chance that at least 3 of them will have an IQ score greater than 125 (use binomial PMF)

Please complete the following problems. Show as much work as you can, and complete the problems as neatly as possible. The x in [x] after each problem denotes the point value.

For each problem, perform the following steps. Assume that all variables are normally or approximately normally distributed.

1. State the hypothesis and identify the claim.

2. Find the critical value(s).

3. Compute the test value.

4. Make the decision.

5. Summarize the results.

5. The heights (in feet) for a random sample of world famous cathedrals are listed below. In addition, the heights for a sample of the tallest buildings in the world are listed. Is there sufficient evidence at α = 0.05 to conclude that there is a difference in the variances in height between the two groups? [4]

1. Maggie buys an MP3 player and loads 10 songs on it: 3 rock, 6 pop, and 3 country songs. She listens to the first two songs in shuffle mode, which picks songs at random and allows the same song to be played repeatedly.
(a) Write the sample space as a set of ordered pairs. (You may abbreviate rock, pop, and country as R, P, and C, respectively.)
(b) Are these outcomes equally likely? Why or why not?

2. Homer rolls two fair dice. As a reduced fraction such as ¼ (not a decimal such as 0.25), find the probability that he rolls each of the following. You must show work!
(a) a sum of at most 5
(b) odd and greater than 8
(c) 3, given that the sum is less than 4

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities:

P(high-quality oil) = .3

P(medium-quality oil) =.5

P(no oil) = .2

a. What is the probability of finding oil (to 1 decimal)? ______

b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below:

P(soil/high-quality oil) = 0.3

P(soil/medium-quality oil) = 0.5

P(soil/no oil) = 0.2

Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).

P(high-quality oil/soil) = _____

P(medium-quality oil/soil) = _____

P(no oil/soil) = ______

What is the new probability of finding oil (to 4 decimals)? _____

According to the revised probabilities, what is the quality of oil that is most likely to be found?

^High quality, medium quality, or no oil?

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Age and movie preference are not independent.
H₁: Age and movie preference are independent.H₀: Age and movie preference are independent.
H₁: Age and movie preference are not independent.    H₀: Age and movie preference are not independent.
H₁: Age and movie preference are not independent.H₀: Age and movie preference are independent.
H₁: Age and movie preference are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

binomialnormal    uniformchi-squareStudent's t

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age of young adult and movie preference are not independent.At the 5% level of significance, there is insufficient evidence to conclude that age of young adult and movie preference are not independent.

Health experts’ estimate for the sensitivity of coronavirus tests, as they are actually used, is 0.7. They also think the specificity is very high. Suppose specificity is 0.99 and that the health experts’ estimated sensitivity is correct (0.7).

a. In a population where 20% of the population is infected with the coronavirus, what is the probability that a person who tests positive actually is infected?

b. Continued. What is the probability that a person who tests negative actually is not infected?

c. If the prevalence of infection in the tested population is 0.8 (in other words, if 80% of people tested have the infection), what is the probability that a person who tests positive actually is infected?

d. Continued. What is the probability that a person who tests negative actually is not infected?

Pesticides sprayed on crops can affect human beings. A symptom of the action of a pesticide is reduction

in brain acetylcholinesterase (AChE) activity, and a severe reduction can be dangerous in terms of body

functions. When cotton is sprayed, one criterion of the existence of such a reduction is whether quail in

field borders show reduced AChE activity. In one collection, the following six observations were made

for brain AChE activity in quail: 86.03, 83.67, 95.21, 92.94, 83.12 and 80.22. Suppose that the mean

brain AChE activity for quail who have not been exposed to the pesticide is 95. Do these data show a

reduction in AChE activity. Test at a 0.05 significance level

A government agency hires you to provide consulting on new rules regarding vehicle license plates. The agency is considering an all-numbers license plate that has six slots (digits 0-9 with no duplicate digits allowed). How many possible license plates are there?

Acceptable license plate: 134-058

Unacceptable license plate: 114-432 (duplicates)

Group of answer choices

1,000,000

248,480

60,480

151,200

3. Using the same table from class (or Appendix C in Priviterra, pp. C1-C4), find the proportion under the standard normal curve that lies between each of the following points:

3. Consider the quality of cars, as measured by the number of cars requiring extra work after assembly, in each day’s production for 15 days:

     30, 34, 9, 14, 28, 9, 23, 0, 5, 23, 25, 7, 0, 3, 24

   a. Find the average number of defects per day.

   b. Find the median number of defects per day.

   c. Find the mode number of defects per day.

   d. Find the quartiles.

   e. Find the extremes.

1. Listed below are the lead concentrations innug/g measured jn different traditional medicines. Use a 0.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 12 ug/g. Assume that the lead concentrations in traditional medicines are normally distributed. What are rhe null and alternatice hypothesis, test statistic, and P-Value.

22, 12.5, 16.5, 6.5, 4.5, 6, 8.5, 4.5, 14.5, 3.5

Assuming the degrees of freedom equals 27, select the t value from the t table.