Approximately 35.73% of all businesses are owned by women. If you take a sample of 105 businesses in Michigan, what is the probability that less than 32.92% of them would be owned by women?

Question 4 options:

Energetic Co., a battery manufacturer, claims their battery lasts for 67.37 months with a standard deviation of 11.583 months. You randomly sample 16 of these batteries. Assuming the distribution for the battery lifetime is approximately normal, what is the probability the average lifetime is greater than 66.54?

Question 9 options:

The F distribution differs from the t distribution is all of these ways except ?

(1 point) A recent poll of 2300 randomly selected 18-25-year-olds revealed that 266 currently use marijuana or hashish. According to a publication, 12.5% of 18-25-year-olds were current users of marijuana or hashish in 1997. Do the data provide sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%? Use α=0.01 significance level.

test statistic z=

positive critical z score    

negative critical z score     

The final conclusion is

A. There is not sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.
B. There is sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.

The following is a short description of the 1854 cholera epidemic of London investigated by Dr. John Snow. Read it and answer the questions that follow.

A total of 862 out of 186,787 people died due to cholera in a sub-district of London during a 48 day period from July 8 to August 26,1854. 844 cholera deaths occurred in a sub-population of 167,654 people using water supplied by Southwark Company, while 18 cholera deaths occurred in 19,133 people using water supplied by Lambeth Company. Dr. John Snow conducted a study of the area and found that each company supplied both rich and poor, both large and small houses, and there were no differences in either the health condition or occupation of the persons receiving the water of the two companies. On the basis of these findings, John Snow argued that drinking water supplied by Southwark Company, whose source was the polluted water of the Thames River, caused the cholera epidemic. Cholera deaths decreased after the water source was changed to less polluted water.

1. Calculate the risk ratio of cholera deaths among people using water supplied by Southwark Company as compared to Lambeth Company.

2. Do you think that this risk ratio is strong enough to support a cause-effect relationship between cholera deaths and water supply? Why or why not?

3. John Snow's study was done long before the identification of the causative organism of cholera-- Vibrio cholera. Thus, Sir Bradford Hill's guideline of biological plausibility was lacking when John Snow did his study. What does this tell you about the nature of the biological plausibility criteria?

4. As you know, temporality is one of the key causal guidelines proposed by Hill. What kind of evidence would need to be provided about the 1854 cholera epidemic to support Hill's guideline about temporality?

5. A marked reduction in cholera deaths occurred after the improvement in water supply. Which one of Hill's guidelines is supported by this fact?

7. a) A study measures how the number of hours of sleep a person gets affects the number of errors they make in a test of short term memory. The regression finds the slope (b) = -3 and the intercept (a) = 25. Interpret the slope in a sentence. Interpret the intercept in a sentence.

b) A study measures how a person’s age (in years) affects the number of messages they get on a dating site. The regression finds the slope (b) = -2 and the intercept (a) = 100. Interpret the slope in a sentence. Interpret the intercept in a sentence.

c) For which of the two studies mentioned above is it more reasonable to interpret the intercept and why?

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