A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement? Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course) . Use a significance level of α=0.01 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course.

Step 1 of 5 : State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

Be honest, have you ever met someone, only to be shocked that you share the same birthday? We have all been there at one point or another. Address this event with a measure of probability.

See, each semester I ask each of my classes of about 32 face-to-face students the question, "What do you believe the probability is that there exists a common birthday(s) among those in this class?" After each person has the opportunity to consult his or her neighbor, I proceed to write down the guesses on the board. Those guesses often look something like this: 1%, 10%, 25%,50%, 67%, 90% 100%. As we all know, only one of these can be correct (if any).

Using your understanding of counting techniques and probability, investigate the answer to this question. What do you calculate to be the true probability of such an event?

A full-service car wash has an automated exterior conveyor car wash system that does the initial cleaning in a few minutes. However, once the car is through the system, car wash workers hand clean the inside and the outside of the car for approximately 15 to 25 additional minutes. There are enough workers to handle four cars at once during this stage. On a busy day with good weather, the car wash can handle up to 150 cars in a 12-hour time period. However, on rainy days or on certain days of the year, business is slow. Suppose 50 days of work are randomly sampled from the car wash’s records and the number of cars washed each day is recorded. A stem-and-leaf plot of this output is constructed and is given below. Study the plot and write a few sentences describing the number of cars washed per day over this period of work. Note that the stem-and-leaf display is from Minitab, the stems are in the middle column, each leaf is only one digit and is shown in the right column, and the numbers in the left column are cumulative frequencies up to the median and then decumulative thereafter.

From the stem and leaf display, the original raw data can be obtained. For example, the fewest number of cars washed on any given day are ____. The most cars washed on any given day are _____. The modal stems are 3, 4, and 10 in which there are ___ days with each of these numbers. Studying the left column of the Minitab output, it is evident that the median number of cars washed is ____. There are only ___ days in which 90 some cars are washed (90 and 95) and only _____ days in which 130 some cars are washed (133 and 137).

6) In a random sample of​ males, it was found that 25 write with their left hands and 209 do not. In a random sample of​ females, it was found that 75 write with their left hands and 454 do not. Use a 0.01 significance level to test the claim that the rate of​ left-handedness among males is less than that among females. Complete parts​ (a) through​ (c) below.

a1) Test the claim using a hypothesis test

Consider the first sample to be the sample of males and the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis​ test?

a2) Identify the test statistic (Round to two decimal places as needed)

a3) Identify the P Value (Round to three decimal places as needed)

a4) What is the conclusion based on the hypothesis?

The P-Value is _____(greater than/less than) the significance level of alpha = 0.01, so _______(fail to reject/reject) the null hypothesis. There is _______(sufficient/is not sufficient) evidence to support the claim that the rate of left-handedness among males is less than that among females.

b1) Test the claim by constructing an appropriate confidence interval.

The 98% confidence interval is ____ < (p1-p2) < ____ (Round to three decimal places as needed)

b2) What is the conclusion based on the confidence interval?

Because the confidence interval limits ______(include/does not include) 0, it appears that the two rates of left-handedness are ____(equal/not equal/equivalent). There is _____(sufficient/not sufficient) evidence to support the claim that the rate of left handedness among males is less than that among females.

c1) Based on the results, is the rate of left handedness among males less than the rate of left handedness among females?

a) The rate of left handedness among males does appear to be less than the rate of left handedness among females because the results are not statistically significant.

b) The rate of left handedness among males does appear to be less than the rate rate of left handedness among females because the results are statistically significant

c) The rate of left handedness among males does not appear to be less than the rate of left handedness among females

d) The results are inconclusive

As you think about the nature of hypothesis testing, making inferences from samples, respond to the quote below. Include in your response an assessment of the benefits of this approach and the drawbacks of this approach.

Statistics may be defined as "a body of methods for making wise decisions in the face of uncertainty."

Please write clear !

A time series model is a forecasting technique that attempts to predict the future values of a variable by using only historical data on that one variable. Here are some examples of variables you can use to forecast. You may use a different source other than the ones listed (be sure to reference the website). There are many other variables you can use, as long as you have values that are recorded at successive intervals of time.

Currency price

GNP

Average home sales

College tuition

Weather temperature or precipitation

Stock price

1.   State the variable you are forecasting.

2.   Collect data for any time horizon (daily, monthly, yearly). Select at least 8 data values.

3.   Use the Time Series Forecasting Templates to forecast using moving average, weighted moving average, and exponential smoothing

4.   Copy/paste the results of each method into your post. Be sure to state the number of periods used in the moving average method, the weights used in the weighted moving average, and the value of α used in exponential smoothing.

5.   Clearly state the “next period” prediction for each method.

Using the data, find the sample skewness and excess kurtosis of Michelson data on the speed of light (light.txt). Is this data set nrmally distribuited, based on this normal probability plot? 850 740 900 1070 930 850 950 980 980 880 1000 980 930 650 760 810 1000 1000 960 960 960 940 960 940 880 800 850 880 900 840 830 790 810 88 880 830 800 790 760 800 880 880 880 860 720 720 620 800 970 950 800 910 850 870 840 840 850 840 840 840 890 810 810 820 800 770 740 760 750 760 910 920 890 860 880 720 840 850 850 780 890 840 780 810 760 810 790 810 820 850 870 870 810 740 810 940 950 800 810 870. a) Find the sample skewness of Michelson data of the speed of light. b)find the excess kurtosis of Michelson data of the speed of light.

the results of a survey in which people from high income countries were asked to report their level of education (less than basic, basic and advanced) and whether they were employed or not. The results are in thousands and are for the 2016-17 period.

You work for a Human Resources firm interested in global employment trends. You randomly sample 30 employed people from high income countries and ask them about their level of education.

a) What is the probability that 24 or fewer of these people would have an advanced education? (Round to 3 decimals)

b) What is the probability that 3 or more of these people would have a less than basic education? (Round to 4 decimals)

c) What is the probability that at least 10 of these people would have a basic education? (Round to 2 decimals)

d) What's the expected number of employed people with a basic education (Round to the nearest integer)?

e) What does this data tell you about employment and education in high income countries?

Find a dataset online, and get a feel for it by performing some EDA. Produce a single plot which you think captures an interesting aspect of the data, and comment on it. (If you wish to use R, there are many data sets already built in, e.g. to the package ‘MASS’; if you are not using R, datasets are readily available -a simple Google search of ’sample datasets’ yields numerous results, for example.)

1.)the chair of the board of directors says, "there is a 50% chance this company will earn a profit, a 30% chance it will lose money next quarter." a.) use an addition rule to find the probability the company will not lose money next quarter B.) use he complement rule to find the probability it will not lose money next quarter.

2.)suoose P(X₁ )=.75 and P(Y₂|X₁)=.40. what is the joint probability of X₁ & Y₂

3.)An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value. (2) decreasing in value, or (3) remaining same value. List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value.

Data were gathered from a simple random sample of cities. The variables are Violent Crime (crimes per 100,000 population), Police Officer Wage (mean $/hr), and Graduation Rate (%). Use the accompanying regression table to answer the following questions considering the coefficient of Police Officer Wage. Complete parts a through d.

Dependent variable is: Violent Crime

R squareds=39.8 % R squared (adjusted)equals=42.1% s=129.6 with 37 degrees of freedom

a) State the standard null and alternative hypotheses for the true coefficient of Police Officer Wage

A) Ho: βOfficer=0

HA: βOfficer>0

B. H0: β Officer does not equal≠0

HA: β Officer=0

C. H0: βOfficer =0

HA: βOfficer<0

D. H0: βOfficer=0

HA: βOfficer≠0 Your answer is correct.

b) What is the t-statistic corresponding to this test?

_______ (Type an integer or a decimal.)

A survey of 25 randomly selected psychiatrists found an average hourly wage (including benefits) of $65.00 per hour. The sample standard deviation was $6.25 per hour. 1. What is the population mean? What is the best estimate of the population mean? 2. Develop a 99% confidence interval for the population mean wage (including benefits) for these psychiatrists. 3. How large a sample is needed to assess the population mean with an allowable error of $1.00 at 95% confidence?

The length, XX, of a fish from a particular mountain lake in Idaho is normally distributed with μ=9.1μ=9.1 inches and σ=2σ=2 inches.

(a) Is XX a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS)
ANSWER:

(b) Write the event ''a fish chosen has a length equal to 6.1 inches'' in terms of XX:  .

(c) Find the probability of this event:

d) Find the probability that the length of a chosen fish was greater than 10.6 inches:  .

(e) Find the probability that the length of a chosen fish was between 6.1 and 10.6 inches: