Consider a general one-sided hypothesis test on a population mean µ with null hypothesis H0 : µ = 0, alternative hypothesis Ha : µ > 0, and Type I Error α = 0.02. Assume that using a sample of size n = 100 units, we observe some positive sample mean x > 0 with standard deviation s = 5. (a) Calculate the Type II Error and the power of the test assuming the following observed sample means: (i) x = 1.5 and (ii) x = 2.0. (b) How does the power of test behave as the observed sample mean x gets further away from the null hypothesis mean µ0?

Chapter 7, Section 2, Exercise 033

Find the expected count and the contribution to the chi-square statistic for the (Group 2, No) cell in the two-way table below. Yes No Group 1 717 272 Group 2 1171 324 Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Expected count=

contribution to the chi-square statistic=

Using R code solve

Here, we look at how t critical values behave as their df (degrees of freedom) increases:

a. First, what is z.05?

b. Second, if you look at t.05,df (t critical values for α = .05) with df = 20, 40, 60, etc (continuing up by 20 each time), for what df does the t critical value first fall strictly within (e.g. < ) i. .05 of z.05? ii. .02 of z.05? iii. .01 of z.05? c. What do you think the difference will be between z.05 and t.05,df as df → ∞?

1 point) A recent study in the Journal of the American Medical Association reported the results of an experiment where 40 overweight individuals followed the Weight Watchers diet for one year. Their weight changes at the end of the year had a mean of x¯=3.1x¯=3.1 kg with a standard deviation of s=5.1s=5.1 kg. We want to use this data to test the claim that the diet has an effect, that is, that the weight change is higher than 0.

1. Which set of hypotheses should be used for testing this claim?
A. H0:μ=0H0:μ=0 vs. Ha:μ>0Ha:μ>0
B. H0:μ=0H0:μ=0 vs. Ha:μ≠0Ha:μ≠0
C. H0:μ=0H0:μ=0 vs. Ha:μ<0Ha:μ<0
D. H0:μ=3.1H0:μ=3.1 vs. Ha:μ>3.1Ha:μ>3.1

2. Which of the following conditions must be met for the hypothesis test to be valid? Check all that apply.

A. There must be at least 5 people who followed the diet for a full year.
B. The sample size must be at least 30 or the population data for weight loss must be normally distributed.
C. The amount each person's weight changed must be independent of the amount other participant's weights changed.
D. The weight loss measurements for people in the sample must be normally distributed.
E. There must be at least 10 people who 'succeeded' on the diet and 10 who 'failed'.

3. Calculate the test statistic:

4. Calculate the p-value:

5. Calculate the effect size, Cohen's dd, for this test: d^=d^=

6. The results of this test indicate we have a...
A. small
B. small to moderate
C. moderate to large
D. large
effect size, and...
A. some evidence
B. extremely strong evidence
C. strong evidence
D. very strong evidence
E. little evidence
that the observed result is not due to chance, assuming the null model is true.

6. A 95% confidence interval for the mean weight change (in kg) for people on this diet is (1.47, 4.73). Which of the statements below is correct?
A. We can be 95% confident that the mean weight loss for the population of people for whom the sample participants are a representative sample is between 1.47 kg and 4.73 kg.
B. We can be confident that 95% of the individuals who follow this diet for one year will lose between 1.47 kg and 4.73 kg.
C. There is a 95% chance that 95% of the individuals in the study who followed the diet for one year lost at least 1.47 kg.

7.1.2

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft.  In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the random variable, population parameter, and hypotheses.

7.1.6

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft.  In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008).  Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%?  State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use.

7.2.4

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft.  In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? Test at the 5% level.

7.2.6

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental," 2008).  Nationally 1 in 88 children are diagnosed with ASD ("CDC features -," 2013).  Is there sufficient data to show that the incident of ASD is more in Arizona than nationally?  Test at the 1% level.

7.3.6

The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #7.3.8 ("SOCR data 2008," 2013).  Countries that are considered high-income have a mean economic dynamism of 60.29.  Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries?  Test at the 5% level.

Table #7.3.8: Economic Dynamism of Middle Income Countries

7.3.8

Maintaining your balance may get harder as you grow older.  A study was conducted to see how steady the elderly is on their feet.  They had the subjects stand on a force platform and have them react to a noise.  The force platform then measured how much they swayed forward and backward, and the data is in table #7.3.10 ("Maintaining balance while," 2013). Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level.

Table #7.3.10: Forward/backward Sway (in mm) of Elderly Subjects

8.1.4

Suppose you compute a confidence interval with a sample size of 100.  What will happen to the confidence interval if the sample size decreases to 80?

8.1.8

In 2013, Gallup conducted a poll and found a 95% confidence interval of the proportion of Americans who believe it is the government’s responsibility for health care.  Give the statistical interpretation.

8.2.6

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental," 2008).  Find the proportion of ASD in Arizona with a confidence level of 99%.

8.3.6

The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #8.3.9 ("SOCR data 2008," 2013).  Compute a 95% confidence interval for the mean economic dynamism of middle-income countries.

Table #8.3.9: Economic Dynamism ($) of Middle Income Countries

The Camera Shop sells two popular models of digital SLR cameras (Camera A Price: 230, Camera B Price: 310). The sales of these products are not independent of each other, but rather if the price of one increase, the sales of the other will increase. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model: NA = 192 - 0.5PA + 0.25PB NB = 305 + 0.08PA - 0.6PB Construct a model for the total revenue and implement it on a spreadsheet. Develop a two-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10.

Max profit occurs at Camera A price of $ _______

Max profit occurs at Camera B price of $ _______

I am doing a kids fishing game. right now I am doing it with 15 fish and number them 1-5. prize one the lowest value and prize 5 the highest value. What do I need to do for this?

You can work with a partner or by yourself. I want you to invent a game with at least 12 different possible monetary outcomes. These outcomes need to include prizes other than money. You are going to charge people money (you decide how much) to play the game and then you decide how much each outcome is worth (win or lose). Make sure that you are able to find the probability of each outcome (Hint: use dice, deck of cards, etc.) Your goal is to come up with an appealing game that people will want to play, but that you will be the one making money in the end. NO RAFFLES.

Title your game, explain the rules, and list the prizes.

Construct a probability distribution in chart form for your game, your random variable x should represent the player’s monetary outcome (there should be at least 12 different x values). Be sure to subtract what you charged to play from their winnings.

Find the player’s expected value of your game. The expected value needs to be between $-2.00 and $0.00.

Explain how this game is going to make you money, but still be appealing enough for people to try and play.

The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a​ correlation? Use a significance level of

alphaαequals=0.05.the award winners.

Construct a scatterplot. A scatterplot has a horizontal axis labeled Best Actress in years from 20 to 70 in increments of 5 and a vertical axis labeled Best Actor in years from 20 to 70 in increments of 5. Twelve points are plotted with approximate coordinates as follows: (27, 44); (30, 39); (28, 40); (58, 47); (31, 50); (34, 49); (46, 56); (30, 47); (61, 39); (22, 55); (43, 44); (54, 34).

Show that the curve C(t) = <a_1, a_2, a₃>t² + <b_1, b_2, b₃>t + <c_1, c_2, c₃> lies in a plane and find the equation for such a plane.

A researcher was interested in how students’ Graduate Record Examinations scores (GREQ- Quantitative and GREV-Verbal) predict college students’ graduate school Grade Point Average (GGPA). He collects data from 30 college students. The GRE Quantitative (X1) and GRE Verbal (X2) scores can range from 400-1600 (Note. This is the old GRE score scale). GGPA (Y) can range from 0.00 to 4.00.

1. If someone were to increase their GRE-Quantitative score by 50 points, how much would you expect his or her GPA to change, after controlling for the GRE-Verbal variability? Show how you calculated your answer. (8 p)

2. In your own words explain why you think that the model did not explain all of the variability in GGPA. In other words, what other factors might play a role in increasing the amount of variability explained in GGPA. (8 p)

3. Which of the two independent variables contributes more weight to the regression equation? In other words, which independent variable contributes more to the explanation of the dependent variable variability? Justify why you believe your answer is correct. (6 p)

4. Report and interpret the Pearson Correlation coefficients between GGPA & GREQ, GGPA & GREV, and GREQ & GREV. (12 p)

The number N of devices that a technician must try to repair during the course of an arbitrary workday is a random variable having a geometric distribution with parameter p = 1/8. We estimate the probability that he manages to repair a given device to be equal to 0.95, independently from one device to another

a) What is the probability that the technician manages to repair exactly five devices, before his second failure, during a given workday, if we assume that he will receive at least seven out-of-order devices in the course of this particular workday?

b) If, in the course of a given workday, the technician received exactly ten devices for repair, what is the probability that he managed to repair exactly eight of those?

c) Use a Poisson distribution to calculate approximately the probability in part (b).

d) Suppose that exactly eight of the ten devices in part (b) have indeed been repaired. If we take three devices at random and without replacement among the ten that the technician had to repair, what is the probability that the two devices he could not repair are among those?

Answer each sub-question by stating whether the term indicated would increase, decrease, stay the same, or not enough info to say. (Note: “increase” and “decrease” refer to the absolute value.)

a) In the binomial distribution, as N decreases, what happens to the value of the most likely outcome when P = .50?

B. For any N, as P increases from .10 to .50, what happens to the value of the most likely outcome?

C. For any N, as P increases from .50 to .90, what happens to the value of the most likely outcome?

D. When P = .5, what happens to the probability of the most likely individual outcome, as N increases?

E. When P = .8, what happens to the probability of the most likely individual outcome, as N increases?

F. In the binomial distribution, what happens to the value of the most likely individual outcome as N increases and, at the same time, P increases?

G) When P = .5, what happens to the individual probabilities of the very most extreme outcomes (that is, the very highest and lowest possible outcomes) as N increases?

Please show work. Thank You.

A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans: 12.15 12.17 12.20 11.88 12.16 12.04 12.05 12.11 Perform a hypothesis test to determine whether the mean volume is greater than 12 ounces. Use the α=0.05 level of significance and the critical value method. Compute the value of the test statistic. Round the answer to three decimal places. t=?

The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of woman receiving prenatal care ("Pregnant woman receiving," 2013). The data for the countries where this information is available for the year 2011 are in table #10.1.8. Find the correlation coefficient and coefficient of determination and then interpret both.