A class survey in a large class for first-year college students asked, "About how many hours do you study in a typical week?". The mean response of the 427 students was x¯¯¯ = 12 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation 7 hours in the population of all first-year students at this university. What is the 99% confidence interval (±0.001) for the population mean?

Confidence interval is from ____to_____ hours.

typical student has a normal distribution with mean of 10 minutes and standard deviation of 2 minutes to complete a question. The total exam has 80 minutes.

how many questions should the exam have so that only 6 in 10,000 students failed the exam?

(that is, p(y>80) = 0.0005)

The birth weight of babies is approximately LOGNORMALLY distributed, with a mean of 3732 grams and a standard deviation of 472 grams.

(a) What is the probability that a baby’s weight exceeds 5000g?
(b) What is the probability that a baby’s weight is between 3000g and 4000g?
(c) What are the 10th, 50th, and 95th percentile weights for a baby?

A sample of 22 observations is selected from a normal population for which the population standard deviation is known to be 8. The sample mean is 27.

a. Determine the standard error of the mean. (Round the final answer to 3 decimal places.)

The standard error of the mean is.

b. Explain why we can use formula (8–1) to determine the 90% confidence interval, even though the sample size is less than 30.

(Click to select)  The population is normally distributed and the population variance is unknown.  The population is normally distributed and the population variance is known.  The population is normally distributed and the sample variance is known.

c. Determine the 90% confidence interval for the population mean. (Round the intermediate calculation to 3 decimal places. Round the final answers to 3 decimal places.)

The 90% confidence interval for the population mean is between and.

Using R Studio/R programming...

1. Usually, we will use a random sample to estimate the statistics of the underlying population. If we assume a given population is a standard normal distribution and we want to estimate its mean, which is the better technique to estimate that mean from a sample:
   1. Use the mean of one random sample of size 500
   2. Use the mean of 300 random samples of size 10

Run your own experiment and use your results as a supporting argument for your response.

How might I run A and B? What is the format? I don't particularly need the answer, I can determine that on my own. I just need help with the "set up". Thanks!

A random sample of 10 observations was drawn from a large normally distributed population. The data is below.

21 26 27 21 19 28 25 25 20 20

Test to determine if we can infer at the 7% significance level that the population mean is not equal to 23, filling in the requested information below.

The p-value is =

Your decision for the hypothesis test:

A. Reject ?0.

B. Reject ?1.

C. Do Not Reject ?1.

D. Do Not Reject ?0.

As part of an environmental studies class​ project, students measured the circumferences of a random sample of 50 blue spruce trees near Brainard​ Lake, Colorado. The sample mean circumference was 30.4 inches. The population standard deviation is known to be around 7.1 inches. Find a 99% confidence interval for the population mean circumference of all blue spruce trees near this lake.

​A) What type of confidence interval are you to​ find?

A.

​1-Sample Mean Interval using Z

B.

​1-Sample Mean Interval using T

C.

None of the Above

​B) Confidence​ Interval: (

nothing

​,

nothing

​)

​(round each interval limit to two decimal​ places)

​C) Interpret the interval in the SHOW YOUR WORK area.

In an earlier study, it was found that the total number of tourists (including adults only) arriving at the island are equally distributed among the four nationalities (BRITISH, GERMAN, FRENCH, ITALIANS).

The new study indicated that that the total number of tourists (including adults only) arriving at the island are distributed among the four nationalities as follows: 26% BRITISH, 27 % GERMAN, 22% FRENCH, 25% ITALIANS

i. State the null and the alternative Hypotheses in order to test if the findings of the earlier study concerning the distribution of visitors among the four main nationalities are still valid.

ii. Test the hypothesis at α = 5%.

iii. What is your conclusion?

A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions. (Round your answers up to the nearest integer.)

(a)

What sample size is necessary if the 95% CI for p is to have a width of at most 0.16 irrespective of p?

(b)

If the legislator has strong reason to believe that at least

of the electorate know of her position, how large a sample size would you recommend to maintain a width of at most 0.16?

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

The worldwide sales of cars from 1981-1990 are shown in the table below. Given: α = 0.2 and β = 0.15 (Hint: Use XLMiner) Year Units sold in thousands 1981 888 1982 900 1983 1000 1984 1200 1985 1100 1986 1300 1987 1250 1988 1150 1989 1100 1990 1200 Using the double exponential smoothing, find the value of the root mean square error for the given data.

Do various occupational groups differ in their diets? A British study of this question compared 95 drivers and 57 conductors of London double-decker buses. The conductors' jobs require more physical activity. The article reporting the study gives the data as "Mean daily consumption ± (se)." Some of the study results appear below. Drivers Conductors

Total calories 2828 ± 44 2842 ± 49

Alcohol (grams) 0.27 ± 0.06 0.44 ± 0.05

What justifies the use of the pooled two-sample t test?

The similarity of the sample means suggests that the population standard deviations are likely to be different.

The similarity of the sample standard deviations suggests that the population standard deviations are likely to be different.

The similarity of the sample means suggests that the population standard deviations are likely to be similar.

The similarity of the sample standard deviations suggests that the population standard deviations are likely to be similar.

Is there significant evidence at the 5% level that conductors consume more calories per day than do drivers? Use the pooled two-sample t test to obtain the P-value. (Give answers to 3 decimal places.)

t =

df =

P-value =

A company samples the distribution of conductivity in isolation of receptacles and got the following values:

24.46 25.61 26.25 26.42 26.66 27.15 27.31 27.54 27.74 27.94 27.98 28.04 28.28 28.49 28.50 28.87 29.11 29.13 29.50 30.88

Trimming 10% mean when we discard the smallest and largest 10 % of the sample. Can we use that sample for to calculate the point estimate of population mean? What are the values for estimator of population mean with and without trim? Provide full reasoning.

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Do professional golfers play better in their last round? Let row B represent the score in the fourth (and final) round, and let row A represent the score in the first round of a professional golf tournament. A random sample of finalists in the British Open gave the following data for their first and last rounds in the tournament.

Do the data indicate that the population mean score on the last round is higher than that on the first? Use a 5% level of significance. (Let d = B − A.)
What is the value of the sample test statistic? (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

The artifact frequency for an excavation of a kiva in Bandelier National Monument gave the following information.

Does this information indicate that there tend to be more flaked stone tools than nonflaked stone tools at this excavation site? Use a 5% level of significance. (Let d = flaked − nonflaked.)

What is the value of the sample test statistic?

ASK YOUR TEACHER

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown below.

It is hypothesized that in winter, "loner" males (not present in summer packs) join the pack to increase survival rate. Use a 5% level of significance to test the claim that the average percentage of males in a wolf pack is higher in winter. (Let d = winter − summer.)
What is the value of the sample test statistic? (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

In the following data pairs, A represents birth rate and B represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information.

Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use α = 0.01. (Let d = A − B.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)