Consider the following data between number of visitors x and the amount of wildlife seen in Cheaha State Park y,

(a) Find the mean of x and the mean of y.

(b) Find the standard deviation of x and the standard deviation of y. Use Excel.

(c) Find the correlation coefficient. Use Excel. (d) Find the slope and intercept of the linear regression line. Then write down the line.

(e) Make predictions for all the values of x in the table. Then calculate the residuals.

(f) Calculate the sum of squared residuals. (g) Calculate the standard deviation of the regression.

(h) Using the mean of x and your data for x, calculate the sum of squared deviations.

(i) Write down an appropriate null and alternative hypothesis.

(j) Calculate the test-statistic.

(k) Make a prediction for when x is 470, and calculate (xp − ¯ x)2. Then make a confidence interval around your prediction.

1. Old Billie is very excited for Letecia, but she is also worried about her. So she conducts a poll of 400 Avocado Park residents who have gone on a first date in the last month and asks them if they are glad they did. Old Billie has decided that she will stop the date from happening if there is less than a 75% chance that Letecia will be happy. Hadey tells her she is being extra, so she settles on a significance level of 0.01 to be safe.
   1. Identify the population of interest.
   2. Identify the variable of interest. What type of variable is it?
   3. What would be a suitable parameter for summarizing the variable you identified in part b?
   4. Write appropriate null and alternative hypotheses for Old Billie’s research goals.
   5. What assumptions must you make to perform a test on the null hypothesis you chose in part d?
   6. Calculate the P-Value and make a decision about the null hypothesis based on it.
   7. Summarize your decision from part f.

A.) A telephone manufacturer finds that the life spans of its telephones are normally distributed, with a mean of 6.7 years and a standard deviation of 0.5 year. (Round your answers to three decimal places.)

What percent of its telephones will last at least 7.25 years?

What percent of its telephones will last between 5.8 years and 6.8 years?

What percent of its telephones will last less than 6.9 years?

B.) The amount of time customers spend waiting in line at the ticket counter of an amusement park is normally distributed, with a mean of 6.5 min and a standard deviation of 1 min.

Find the z-score for the following data value 8 min.

Find the probability that a customer will wait less than 8 minutes. (Round your answer to three decimal places.)

Find the z-score for the following data value 6 min.

Find the probability that a customer will wait less than 6 minutes. (Round your answer to three decimal places.)

The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?

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State the null and alternate hypotheses.

H0: Age distribution and location are independent.

H1: Age distribution and location are not independent.

H0: Age distribution and location are not independent.

H1: Age distribution and location are not independent.

H0: Age distribution and location are not independent.

H1: Age distribution and location are independent.

H0: Age distribution and location are independent.

H1: Age distribution and location are independent.  

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

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1. For each of the following, define the random variable using words, tell what kind of distribution each has, and calculate the probabilities. Every day when Sally drives to school, she has a 70% chance of not finding a parking spot in the closest lot to her classroom (otherwise, she finds a spot). Each day is independent, meaning that finding a spot on one day doesn’t change the probability of finding a spot on any other day.

(a) (3 points) What is the probability that the tenth day is the fifth day that she gets a spot in the closest lot?

(b) (3 points) What is the probability that the tenth day is the first day that she gets a spot in the closest lot?

(c) (3 points) What is the probability that the she gets to park in the closest lot in 5 out of the next 10 days?

(d) (3 points) If she parks in the close lot at least 3 times in a week (5 days), she will treat herself to ice cream. What is the probability that she gets ice cream?

Coffee is a leading export from several developing countries. When coffee prices are high, farmers often clear forest to plant more coffee trees. Here are data on prices paid to coffee growers in Indonesia and the rate of deforestation in a national park that lies in a coffee-producing region for five years: Price(cents per pound) Deforestation (percent) 29 0.49 40 1.59 54 1.69 55 1.82 72 3.10 (a) Make a scatterplot. What is the explanatory variable? What kind of pattern does your plot show? (b) Find the correlation r step-by-step. That is, find the mean and standard deviation of the two variables. Then find the five standardized values for each variable and use the formula for r.

Explain how your value for r matches your graph in (a). (c) Now enter these data into your calculator or Excel and use the correlation function to find r. Check that you get the same result as in (b). PLEASE, GIVE A DETAILED SOLUTION. THANK YOU IN ADVANCE!

Suppose that the current market price of VCRs is $300, that the average consumer disposable income is $30,000, and that the price of DVDs (a substitute for VCRs) is $500. Under these conditions annual U.S. demand for VCRs is 5 million per year. Statistical studies have shown that for VCRs the own-price elasticity of demand is –1.3. The income elasticity of demand for VCRs is 1.7. The cross-price elasticity of demand for VCRs with respect to DVDs is 0.8.

Use this information to predict the annual number of VCRs sold under the following conditions:

(a) Increasing competition from Asia causes VCR prices to fall to $270 with income and the price of

       DVDs is unchanged.

(b) Income tax reductions raise average disposable personal income to $31,500 with prices unchanged.

      (Do not use $31.5 for $31,5000!)

(c) An inventor in Menlo Park invents a cheaper way to produce DVDs, reducing the price of a DVD to

      $400, with the price of VCRs and income unchanged.

(d) All of the events described in parts (a)-(c) occur simultaneously.

Recently, the power of cloning to rescue endangered or extinct species was demonstrated by applying nuclear transfer methods to save the mouflon, a species of wild sheep (left half of figure). This result piqued a fair amount of general interest, because of its possible implications for the return of other, more exotic, species from the jaws of extinction (as pictured on the right). Suppose a wealthy investor came to you with a proposal to create a real-life Jurassic Park (naturally, with far more detailed strategy to contain the animals), asking for your scientific analysis of their plan to use SCNT to bring back dinosaurs.

a. Considering all of the materials and technical steps involved in the process of nuclear transfer, list three problems you envision will be encountered by their team of scientists.

b. Speculate on how a researcher might overcome each of the obstacles you identified in (a), or state why you feel they may be insurmountable.

c. Given your analysis in (a) and (b), briefly comment on whether you think that the wealthy investor’s plan is feasible.

Identify the UCS, UCR, CS, and CR in the following examples: