The mean per capita consumption of milk per year is 132 liters with a variance of 625. If a sample of 196 people is randomly selected, what is the probability that the sample mean would differ from the true mean by more than 5.15 liters? Round your answer to four decimal places.

Meteorology: Storms Weather-wise magazine is published in association with the American Meteorological society. Volume 46, Number 6 has a rating system to classify Nor’easter storms that frequently hit New England states and can cause much damage near the ocean coast. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a Nor’easter is in progress at the severe storm class rating.

(a) Let us say that we want to set up a statistical test to see if the wave action (i.e, height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?

(b) If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?

(c) If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?

(d) Suppose you do not know if the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height is different (either higher or lower) from the severe storm class rating. What would you use for the alternate hypothesis?

(e) For each of the tests in parts (b), (c), and (d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.40 ml/kg for the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is unknownσ is knownthe distribution of weights is normaln is largethe distribution of weights is uniform

(c) Interpret your results in the context of this problem.

1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.    The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.90 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)
male firefighters

Suppose that you are testing the hypotheses Upper H 0​: pequals0.22 vs. Upper H Subscript Upper A​: pnot equals0.22. A sample of size 350 results in a sample proportion of 0.28. ​a) Construct a 95​% confidence interval for p. ​b) Based on the confidence​ interval, can you reject Upper H 0 at alphaequals0.05​? Explain. ​c) What is the difference between the standard error and standard deviation of the sample​ proportion? ​d) Which is used in computing the confidence​ interval?

(Note that an Ace is considered a face card for this problem)
In drawing a single card from a regular deck of 52 cards we have:

(a) P( black and a face card ) =
(b) P( black or a face card ) =
(c) P( black or a 3 ) =
(d) P( Queen and a 3 ) =
(e) P( black and a Queen ) =

Each person in a large sample of German adolescents was asked to indicate which of 50 popular movies they had seen in the past year. Based on the response, the amount of time (in minutes) of alcohol use contained in the movies the person had watched was estimated. Each person was then classified into one of four groups based on the amount of movie alcohol exposure (groups 1, 2, 3, and 4, with 1 being the lowest exposure and 4 being the highest exposure). Each person was also classified according to school performance. The resulting data is given in the accompanying table.

Assume it is reasonable to regard this sample as a random sample of German adolescents. Is there evidence that there is an association between school performance and movie exposure to alcohol? Carry out a hypothesis test using

α = 0.05.

State the null and alternative hypotheses.

H₀: Alcohol exposure and school performance are not independent.
H_a: Alcohol exposure and school performance are independent. H₀: The proportions falling into the alcohol exposure categories are not all the same for the three school performance groups.
H_a: The proportions falling into the alcohol exposure categories are the same for the three school performance groups.     H₀: The proportions falling into the alcohol exposure categories are the same for the three school performance groups.
H_a: The proportions falling into the alcohol exposure categories are not all the same for the three school performance groups. H₀: Alcohol exposure and school performance are independent.
H_a: Alcohol exposure and school performance are not independent.

Calculate the test statistic. (Round your answer to two decimal places.)
χ² =

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =

What can you conclude?

Do not reject H₀. There is not enough evidence to conclude that there is an association between alcohol exposure and school performance. Reject H₀. There is convincing evidence to conclude that there is an association between alcohol exposure and school performance.      Do not reject H₀. There is not enough evidence to conclude that the proportions falling into the alcohol exposure categories are not all the same for the three school performance groups. Reject H₀. There is convincing evidence to conclude that the proportions falling into the alcohol exposure categories are not all the same for the three school performance groups.

You may need to use the appropriate table in Appendix A to answer this question.

In a random sample of 24 fifth graders who took an IQ test, the average score was 101.48 with a standard deviation of 13.34. Assuming that the IQ scores are normally distributed, what will be the 98% confidence interval for the average IQ scores for all fifth graders?

Select the best answer.

96.3054 to 106.6546

95.5521 to 107.4079

96.8131 to 106.1469

94.6728 to 108.2872

total, 16 patients were enrolled in the study. Values of the f-wave frequency during day- and night-time are given in the table below.

Data analysis.

1. Summarize the data.

(decide which sampling technique was used to collect the data;

check if the data is normally distributed and if the variances of the groups are similar;

present data graphically; briefly interpret the results)

The slope of a regression tells us:

1. The covariance of X and Y
2. The marginal impact of X on Y
3. The marginal impact of Y on X
4. The level of X when Y is zero
5. The level of Y when X is zero

2. The intercept of a regression tells us:

1. The level of Y when X is zero
2. The level of X when Y is zero
3. The marginal impact of Y on X
4. The marginal impact of X on Y
5. The covariance of X and Y

3. ∑(Y – Ŷ)² is essentially a measure of

1. How much our predictions miss the actual data
2. How much variance we explain with X
3. How much variance we explain with Y
4. The covariance between the prediction and X
5. How much our predictions deviate from X

4. The main difference between the calculation of Pearson’s r and the slope of a regression is

1. The inclusion of the covariance in the numerator
2. The inclusion of the SSx in the denominator
3. The inclusion of the SSy in the denominator
4. The inclusion of the SSx in the numerator
5. The inclusion of the SSy in the numerator

5. A regression with a slope of 4 tells us

1. The slope is large and significant
2. The slope is large but not significant
3. The slope is small and significant
4. The slope is small and not significant
5. Not enough information to decide

6. A significance test for beta that fails to reject the null

1. Cannot distinguish beta from zero
2. Lacks sufficient information to make a decision
3. Can distinguish beta from zero
4. Tells us that beta is negative
5. Tells us we have made a Type I Error

The slope of a regression tells us:

1. The covariance of X and Y
2. The marginal impact of X on Y
3. The marginal impact of Y on X
4. The level of X when Y is zero
5. The level of Y when X is zero

2. The intercept of a regression tells us:

1. The level of Y when X is zero
2. The level of X when Y is zero
3. The marginal impact of Y on X
4. The marginal impact of X on Y
5. The covariance of X and Y

3. ∑(Y – Ŷ)² is essentially a measure of

1. How much our predictions miss the actual data
2. How much variance we explain with X
3. How much variance we explain with Y
4. The covariance between the prediction and X
5. How much our predictions deviate from X

4. The main difference between the calculation of Pearson’s r and the slope of a regression is

1. The inclusion of the covariance in the numerator
2. The inclusion of the SSx in the denominator
3. The inclusion of the SSy in the denominator
4. The inclusion of the SSx in the numerator
5. The inclusion of the SSy in the numerator

5. A regression with a slope of 4 tells us

1. The slope is large and significant
2. The slope is large but not significant
3. The slope is small and significant
4. The slope is small and not significant
5. Not enough information to decide

6. A significance test for beta that fails to reject the null

1. Cannot distinguish beta from zero
2. Lacks sufficient information to make a decision
3. Can distinguish beta from zero
4. Tells us that beta is negative
5. Tells us we have made a Type I Error

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken ten blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.89 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is knownnormal distribution of uric acidn is largeσ is unknownuniform distribution of uric acid

(c) Interpret your results in the context of this problem.

There is not enough information to make an interpretation.The probability that this interval contains the true average uric acid level for this patient is 0.05.    There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.The probability that this interval contains the true average uric acid level for this patient is 0.95.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.02 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

A bag contains 10 blue marbles, 15 red marbles and 20 green marbles. Marbles are then chosen at random.

a) Find the probability of getting a red and then a green marble.

b) Find the probability of getting a red or a green marble.

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers )of the earthquake below the surface at the epicenter. The following is based on information taken from the national earthquake information service of the U.S. Geographical Survey. Additional data may be found by visiting the website for the service.

x 2.9 4.2 3.3 4.5 2.6 3.2 3.4

y 5.0 10.0 11.2 10.0 7.9 3.9 5.5

test on correlation using 0.05 significance

A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ² of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ² = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 14.4 months (squared). Using a 0.05 level of significance, test the claim that σ² = 23 against the claim that σ² is different from 23.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 23; H₁: σ² > 23H_o: σ² = 23; H₁: σ² < 23    H_o: σ² > 23; H₁: σ² = 23H_o: σ² = 23; H₁: σ² ≠ 23

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a normal population distribution.We assume a uniform population distribution.    We assume a exponential population distribution.We assume a binomial population distribution.

(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?

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 insufficient evidence to conclude that the variance of battery life is different from 23.At the 5% level of significance, there is sufficient evidence to conclude that the variance of battery life is different from 23.    

(f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.)

(g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

Suppose a random sample of size 40 is selected from a population with  = 11. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

1. The population size is infinite (to 2 decimals).
   
   
2. The population size is N = 50,000 (to 2 decimals).
   
   
3. The population size is N = 5,000 (to 2 decimals).
   
   
4. The population size is N = 500 (to 2 decimals).

When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the​ environment, 354 of 1180 subjects said yes. a. Find the point estimate of the proportion of the population who would answer yes. b. Find the margin of error for a​ 95% confidence interval. c. Construct the​ 95% confidence interval for the population proportion. What do the numbers in this interval​ represent? d. State and check the assumptions needed for the interval in ​(c) to be valid.

a. Find the point estimate of the proportion of the population who would answer yes. ModifyingAbove p with caretequals ​(Round to five decimal places as​ needed.)

b. Find the margin of error for a​ 95% confidence interval. ​(Round to five decimal places as​ needed.)

c. Construct the​ 95% confidence interval for the population proportion. ​(Round to five decimal places as​ needed.)