(a) A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected and the amount of gas (therms) used during the month of January is determined for each house. The resulting observations are 118, 122, 146, 80, 141, 103, 138, 99, 109, 125. Let μ denote the average gas usage during January by all houses in this area. Compute a point estimate of μ.
therms

(b) Suppose there are 20,000 houses in this area that use natural gas for heating. Let τ denote the total amount of gas used by all of these houses during January. Estimate τ using the data of part (a).
therms

(c) Use the data in part (a) to estimate p, the proportion of all houses that used at least 100 therms.


(d) Give a point estimate of the population median usage (the middle value in the population of all houses) based on the sample of part (a).
therms

Research indicates that the color red increases men’s attraction to women (Elliot & Niesta, 2008). In the original study, men were shown women’s photographs presented on either a white or red background. Photographs presented on red were rated significantly more attractive than the same photographs mounted on white. In a similar study, a researcher prepares a set of 30 women’s photographs, with 15 mounted on a white background and 15 mounted on red. One picture is identified as the test photograph and appears twice in the set, once on white and once on red. Each male participant looks through the entire set of photographs and rates the attractiveness of each woman on a 10-point scale. The following table summarizes the ratings of the test photograph for a sample of nine men. Are the ratings for the test photograph significantly different when it is presented of a red background compared to a white background?

1. State the null and alternative hypotheses
2. Compute the test statistic using SPSS
3. What is the effect size (you will need to compute both Cohen’s d from data given in the SPSS output table)

Cohen’s d= M1 – M2/ ((SD1+SD2) /2)

4. Write the Results section for your findings. Include the descriptive statistics, type of statistical test and results of the test and the confidence interval.

The white wood material used for the roof of an ancient temple is imported from a certain country. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at a university conducted a study to estimate the mean bending strength of the white wood roof. A sample of 16 pieces of the imported wood were tested and yielded the statistics x̄ = 74.6 and s = 9.8 on breaking strength (MPa). Estimate the true mean breaking strength of the white wood with a 95% confidence interval. Interpret the result.

Find the 95% confidence interval for the true mean breaking strength of the white wood.

(___,___) (round to 2 decimal places)

A study of college football games shows that the number of holding penalties assessed has a mean of 2.2 penalties per game and a standard deviation of 1.05 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.15 penalties per game or less?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places

A “subliminal” message is below our threshold of awareness but may nonetheless influence us. A study looked at the effect of subliminal messages on math skills. Messages were flashed on a screen too rapidly to be consciously read. Twenty-eight students who had failed the mathematics part of the City University of New York Skills Assessment Test were randomly assigned to receive daily either a positive subliminal message (“Each day I am getting better in math”) or a neutral subliminal message (“People are walking on the street”). All students took the assessment test again at the end of the program, and the table below gives the data on each of the subjects’ scores before and after the program. Is there statistical evidence that the positive message brought about a greater improvement in math scores than the neutral message? Make no assumptions and show all work.

Got the data by Excel

Naive Bayes Theorem

See the dataset D in Table 1. It consists of clinical data about 14 patients. Using the data in D, determine the Naive Bayes classifier and predict the patients in Table 2. Then, compare with your ‘predicted’ ones with the ground-truth label (i.e., column ’Disease’) and report the accuracy P.

Table 1: Dataset D with clinical data of 14 patients

Table 2: Test data with additional 5 patients

In a developing country, 19% of the entire population has high
speed access to the internet. Random samples of size 200 are selected from the country’s
population in order to estimate the proportion of the population with high-speed internet
access.
a) What is the expected sample proportion? (Do not use the CLT.)
b) What is the standard deviation of the sample proportion? (Do not use the CLT.)
c) What is the probability that the sample proportion is (strictly) less than 14%? (Do not
use the CLT.)
d) Use the Central Limit Theorem (CLT) to estimate the probability that the sample
proportion is between 9% and 29%?
e) Use the CLT to estimate the value p such that the probability that the sample propor
tion is above p is 90%.

Note : Please explain C in details

It is estimated that approximately 8.17% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 98% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 3% of all adults over 40 without diabetes as having the disease. a) Find the probability that a randomly selected adult over 40 does not have diabetes, and is diagnosed as having diabetes (such diagnoses are called "false positives"). b) Find the probability that a randomly selected adult of 40 is diagnosed as not having diabetes. c) Find the probability that a randomly selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes (such diagnoses are called "false negatives"). (Note: it will be helpful to first draw an appropriate tree diagram modeling the situation)

A new car dealer calculates that the dealership must average more than 4.5% profit on sales of new cars. A random sample of 81 cars yielded a sample mean of 4.97% profit and a sample standard deviation of 1.8%. Using a significance level of α = .05, does the sample data provide evidence to conclude that the dealership averages more than 4.5% profit on sales of new cars?

A. Yes, because the the sample mean is more than 4.5%.

B. Yes, because p = .0106 is less than .05.

C. No, because t = 2.35 is more than 1.645

D. No, because the p-value is less than the critical value

Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150°F, there will be no negative effects on the river's ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150°F, researchers will take 50 water specimens at randomly selected times and record the temperature of each specimen. The resulting data will be used to test the hypotheses

H₀: μ = 150°F

versus

H_a: μ > 150°F.

(a) In the context of this example, describe Type I and Type II errors. (Select all that apply.)

A Type I error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F.

A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F.

A Type II error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F.

A Type II error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F.

A magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars).

The mean price of this hamburger in the U.S. in January was $4.61. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at a university used a proposed new computer mouse design. While using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are given. Use these data to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. (Use

α = 0.05.

Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

Each round of game played by a gambler is either a win with probability p or a loss with probability 1 − p. If the round is a win, then a random amount of money having an exponential distribution with rate λ will be awarded to the gambler. If the round is a loss, then he loses everything that had been accumulated up to that time and cannot play any additional rounds. After a win round, the gambler can either choose to quit and keep whatever has been won or can choose to play another round. Suppose that a gambler plans to continue playing until either his total winnings exceeds t or a loss occurs.

(a) What is the expectation of N, the number of winning rounds that it would take until his fortune 1 exceeds t?

(b) What is the probability he will successfully reach a fortune of at least t?

Not handwriting answer, please

In a word document, please answer the following questions:

Course Introduction of Biostatistics

Define the following terms:
correlation coefficient
scatter plot
bivariate relationship
Provide an example where the outlier is more important to the research than the other observations?
Identify when to use Spearman’s rho.

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 231

accurate orders and

74

that were not accurate.a. Construct a

95​%

confidence interval estimate of the percentage of orders that are not accurate.b. Compare the results from part​ (a) to this

95​%

confidence interval for the percentage of orders that are not accurate at Restaurant​ B:

0.2160 <p<0.319

What do you​ conclude?

a. Construct a

95​%

confidence interval. Express the percentages in decimal form.

nothing less than<pless than<nothing

​(Round to three decimal places as​ needed.)

To navigate on Lake Latte (fed by the Decaf and the Vanilla Rivers) at least two of the three
radio navigation beacons must be working. If the probability that a beacon is working is
p and the operational status of each station is independent of the other two, what is the
probability of being able to navigate on the lake? What is the probability that beacon #2 is
working if navigation on the lake is possible?