Shown below is a portion of a computer output for a regression analysing relating Y(dependent variable) and X(independent variable)

ANOVA

df SS

Regression    1    115.064

Residual 13    82.936

Coefficient    Standard error

Intercept 15.532    1.457

X -1.106 0.761

Required :- A) Perform a t test using the p value approach and determine whether x and y are related Let alpha=0.5 . B) Using the p value approach, perform an F test and determine whether x and y are related. C) Compute the coefficient of determination and fully interpret its meaning. Be specific.

Suppose a coin is biased. Specifically, the probability that the flip shows as heads is a random variable P with the probability density function f P(p) = 2(1−p) for 0 ≤ p ≤ 1. Let N be the number of heads in n independent flips of the coin. Find E [ N ] using iterated expectation.

(6.29 & 6.67) Strategic placement of lobster traps is one of the keys for a successful lobster fisherman. An observations study of teams fishing for the red spiny lobster in Baja Cali- fornia Sur, Mexico, was conducted and the results published in Bulletin of Marine Science (April 2010). One of the variables of interest was the average distance separating traps - called trap spacing - deployed by the same team of fishermen. Consider the trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen: 93, 99, 105, 94, 82, 70, 86. Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico.

a. Identify the target parameter for this study.

b. Compute a point estimate of the target parameter.

c. What is the problem with using the standard normal statistic to find a confidence interval for the target parameter?

d. Find a 95% confidence interval for the target parameter.

e. Give a practical interpretation of the interval in part above.

f. What conditions must be satisfied for the interval in part (d) to be valid?

The lifetime of lightbulbs that are advertised to last for 3900 hours are normally distributed with a mean of 4100 hours and a standard deviation of 300 hours. What is the probability that a bulb lasts longer than the advertised figure?

or Exercises 5 through 20, assume that all variables are approximately normally distributed. Stress Test Results For a group of 12 men subjected to a stress test situation, the average heart rate was 109 beats per minute. The standard deviation was 4. Find the 99% confidence interval of the population mean.

The overhead reach distances of adult females are normally distributed with a mean of

205.5 cm

and a standard deviation of

8.6 cm

a. Find the probability that an individual distance is greater than

214.80cm.

b. Find the probability that the mean for

25

randomly selected distances is greater than 204.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

A researcher would like to determine whether an over-the-counter herbal nasal spray has an effect on mental alertness for infants. A sample of n = 16 infants is obtained, and each baby is given a standard dose of the spray one hour before being tested for mental alertness. For the general population of infants, scores on a mental alertness screening test are normally distributed with μ = 60. The infants in the sample had an average score of M = 56.5 and an s = 8.

Can the researcher conclude that scores on the screening test are significantly different after administering the spray? Use a two-tailed test with α = .05. Be sure to state your null hypothesis, a decision about that null hypothesis, and a conclusion explaining your results with an APA format statement. Calculate Cohen’s d if necessary.

the college bookstore says that the average cost of textbooks is $52 with a standard deviation of $4.50. a group of skeptical statistics students want to test the bookstore’s claim with a sample of 100 books, and find a mean of $53. a) what decision should the students make if they set alpha to .01?

b.) Compare and contrast the benefits and drawbacks of having a high alpha level vs. a low alpha level. What are some of the practical/real world implications of either setting an alpha level too high (i.e., .1) or too low (i.e., .001) in your study/analysis?

The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 35 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $39, and the standard deviation for female consumers is assumed to be $20.

1. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
2. At 99% confidence, what is the margin of error (to 2 decimals)?
3. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
   (  ,  )

A small hair salon in Denver, Colorado, averages about 50 customers on weekdays with a standard deviation of 8. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $2 discount on 5 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 5 weekday period jumps to 57. [You may find it useful to reference the z table.]

a. What is the probability to get a sample average of 57 or more customers if the manager had not offered the discount? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

It is known that 5% of the radio tubes produced by a certain manufacturer are defective. If the manufacturer sends out lots containing 100 tubes, what is the probability that at least 98% of the

tubes are good?

1. Flu cases this past flu season in the Remulak school system (n = 500) were 15 per week. For the entire state, the weekly average was 16, and the standard deviation was 15.1. Are the kids in Remulak as sick as the kids throughout the state?
2. The night-shift workers in three of Super Bo's specialty stores stock about 500 products in about 3 hours. How does this rate compare with the stocking done in the other 97 stores in the chain, which average about 496 products stocked in 3 hours? Are the stockers at the specialty stores doing a “better than average” job? Here's the info that you need:

PLEASE ANSWER THE THREE QUESTION WITH CORRCT DEATILAS

Who may request a copy of a birth and death certificate?

If the mother is not married, can the father’s name be placed on the birth certificate?

What does father need to sign in order to be placed on birth certificate of unwed mother?

The cost of adding a new communication node at a location not currently included in the network is of concern to a major manufacturing company. To try to predict the price of new communication nodes, data were obtain on a random sample of existing nodes.

We have information on the following variables:

?: Installation cost of the node, in U.S. dollars (COST)

?1: Number of ports available for access (NUMPORTS)

?2: Bandwidth (BANDWIDTH)

?3: Port speed (PORTSPEED)

Use MINITAB to answer the following questions.

COST NUMPORTS BANDWIDTH PORTSPEED
52388 68 58 653
51761 52 179 499
50221 44 123 422
36095 32 38 307
27500 16 29 154
57088 56   141 538
54475 56 141 538
33969 28 48 269
31309 24 29 230
23444 24 10 230
24269 12 56 115
53479 52 131 499
33543 20 38 192
33056 24 29 230

Perform a global F-test by completing the following steps:

a. The null hypothesis is ?0: ?1 = ?2 = ?3 = 0, what is the alternative hypothesis?

b. What is the p-value for this test?

c. Is there evidence that at least one explanatory variable (number of ports, bandwidth, or port speed) is useful in explaining the variation in the installation cost for communication nodes? (Circle one) i. Yes ii. No

d. What is the value of the MSE for the full model?

Consider the experiment of rolling two dice (six sides each dice). Consider the

following events:

A = the sum is less than or equal to four

B = the sum is a prime number greater than five

C = the sum is greater than or equal to nine

D = the sum is an even number

Determine:

1) P (A or B)

2) P (B and C)

3)P (D / C)