A normal population has a mean of 58 and a standard deviation of 13. You select a random sample of 25.

In a study investigating the difference in food preferences between men and women, researchers asked subjects to indicate whether they like or disliked certain foods. One question was about lamb. Twenty percent of a sample of 75 men disliked lamb, while 38% of a sample of 100 women indicated that they disliked lamb. Test the claim that there is a difference in the proportions of men and women who dislike lamb.

Indicate the correct set of statistical hypotheses for this test.

What is the test statistic?

What is the p-value for this test?

What is your decision regarding the null?

Provide the confidence interval.

Please describe why the confidence interval and hypothesis test are consistent.

7. When you submit your tax return to the IRS, they screen your return for indications of fraud. Naturally the screening system is not perfect: only 92% of fraudulent tax returns get red-flagged (that is, the IRS’ system detects the fraud), and 9% of honest tax returns get red-flagged (the system mistakenly believes these good returns to be fraudulent). A tax return the IRS believes not to be fraudulent is said to be “green-flagged.” Suppose that 4% of all tax returns are fraudulent. (a) What percent of all tax returns are correctly flagged?

(b) If a tax return is red-flagged, what is the probability this return is fraudulent?

(c) The answer to part (b) might worry an administrator at the IRS (or a taxpayer, for that matter!). Briefly explain what causes the answer to part (b) to be somewhat low.

Invest in science ~ The Pew Research Center conducted a survey of U.S. adults in 2019 to determine how American citizens feel about whether federal government should increase spending for scientific research. In the study, there were 712 Democrats and 652 Republicans. According to the survey, 438 Democrats and 270 Republicans said they are in favor of increased spending for scientific research.

We want to estimate the actual difference between the proportions of Democrats and Republicans who favor increased spending for scientific research.

Notation: 1=Democrats and 2=Republicans.

Based on this data, what is the upper bound for a 95% confidence interval for the difference in the population proportions, p1−p2p1-p2

"A producer of various feed additives for cattle conducts a study of the number of days of feedlot time required to bring beef cattle to market weight. Eighteen steers of essentially identi- cal age and weight are purchased and brought to a feedlot. Each steer is fed a diet with a specific combination of protein content, antibiotic concentration, and percentage of feed supplement. The data are as follows:

STEER   PROTEIN ANIBIO  SUPPLEM TIME
1       10      1       3       88
2       10      1       5       82
3       10      1       7       81
4       10      2       3       82
5       10      2       5       83
6       10      2       7       75
7       15      1       3       80
8       15      1       5       80
9       15      1       7       75
10      15      2       3       77
11      15      2       5       76
12      15      2       7       72
13      20      1       3       79
14      20      1       5       74
15      20      1       7       75
16      20      2       3       74
17      20      2       5       70
18      20      2       7       69

8. Calculate the coefficient of determination and interpret.

9. Suppose x1 = PROTEIN, x2 = ANTIBIO and x3 = SUPPLEM, and you enter these predictors in the model in the order of x1, x2, x3. Find SSR(x2 | x1) and SSR(x3 | x1, x2). What do they mean?

10. Test whether adding ANTIBIO and SUPPLEM provides any additional predictive value, given that PROTEIN is already in the model. Include all steps of a statistical test.

Neuroinvasive West Nile virus refers to a severe disease that affects a person’s nervous system. It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1021 reported cases, and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Can we conclude that the 2011 proportion of neuroinvasive West Nile virus cases is significantly more than the 2010 proportion of neuroinvasive West Nile virus cases? If you conduct hypothesis testing, you have to consider:

Group of answer choices

a test of two proportions

a test of two independent means

a test of a single mean

a test of a single proportion.

how does sampling variation relate to concluding Ho or H1 when conducting a hypothesis testing?

1. Suppose box 1 has four black marbles and two white marbles, and box 2 has two black marbles and five marbles. If you picked one marble from one of the two boxes at random, what it the probability that you picked from box 1 given that the marble you picked is black?

2. A raffle has 5000 tickets with the following prizes: 1 ticket has $2000 prize, 10 tickets have $200 prize, and 20 tickets have $50 prize and 500 tickets have a $20 prize. If to buy a ticket costs $15, and X is the random variable that measures net profit:

1. Calculate the pdf table of X
2. Calculate E(X), Var(X)

The average life of light bulbs produced by SABA Electric Co. is expected to be normally distributed with the mean service life of 950 hours and standard deviation of 100 hours. A random sample of 100 bulbs is tested and it has a mean life of 910 hours. Can researcher conclude that the mean service life of the bulbs is less than the expectation? H0 is null hypothesis, and Ha is alternative hypothesis.

Which one of the following is a correct conclusion based on the given data?

Group of answer choices

Reject H0. The mean service life of the bulbs is less than the expectation.

Do not reject H0. The mean service life of the bulbs is less than the expectation.

Reject H0. The mean service life of the bulbs is not less than the expectation

Do not reject H0. The mean service life of the bulbs is not less than the expectation

None of the above.

The annual salaries of 16 randomly chosen actuaries are listed below. At a=0.01 can you conclude that the standard deviation of the annual salaries is greater than $ 20,000 question mark Use the​ P-value method to perform the hypothesis test. 89,480 45,584 58,984 92,296 61,088 40,176 110,016 48,688 103,672 95,992 61,808 46,024 52,944 103,696 55,064 49,568

Find the area under the standard normal distribution curve between =z−1.86 and =z−2.38. Use The Standard Normal Distribution Table and enter the answer to 4 decimal places.

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 427 gram setting. It is believed that the machine is underfilling the bags. A 49 bag sample had a mean of 421 grams. Assume the population standard deviation is known to be 16. A level of significance of 0.1 will be used.

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P P -value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

9. In 2001, a total of 15,555 homicide deaths occurred among males and 4,753 homicide deaths occurred among females. The estimated 2001 midyear populations for males and females were 139,813,000 and 144,984,000, respectively. (10 points)

A. Calculate the homicide-related death rates for males and for females.

B. What type(s) of mortality rates did you calculate in Question 9 A?

C. Calculate the ratio of homicide-mortality rates for males compared to females.

D. Interpret the rate you calculated in Question C as if you were presenting information to a policymaker.

For many years, TV executives used the guideline that 30% of the audience were watching each of the traditional bi three prime-time networks, and 10% were watching cable stations on a weekday night. A random sample of 500 homes in the Tampa-St. Petersburg area last night showed that 165 homes were tuned into the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At the .05 significance level, can we conclude that the national guideline is still reasonable? Show your work.

The following data were randomly drawn from an approximately normal population.

Based on these data, find a 95% confidence interval for the population standard deviation. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places.