Question 3

To estimate the population mean weight of out-going packages, a shipping company randomly samples 70 packages and finds a mean weight of 52 pounds. The population standard deviation is known to be 10.1 pounds.

Construct the 88% confidence interval and state the lower bound ___________________ and upper bound ___________________ , each rounded to the nearest thousandths place.

Interpret your CI in context ___________________.

Question 4

A landscape engineer claims that the average area of a pond is at most 150 sqft. To test this claim 30 randomly selected ponds show a mean of 151.7 sqft. The population standard deviation is known to be 6.8 sqft. Use the pvalue method to test the claim at the 7% significance level.

a. State Ho and Ha ___________________

b. Determine Critical Value and identify the rejection region ___________________

c. State the test menu and determine Test Statistic ___________________

d. Determine the p-value ___________________

e. State the conclusion, explain why, and interpret in context ___________________

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QUESTION 2 what is the main difference between a paired-sample T-test and a one-sample T-Test? ) 1-sample t-test compares one sample mean to a null hypothesis value. A paired t-test calculates the difference between paired observations Oa 1-sample t-test compares one sample mean to another sample mean. A paired t-test calculates the difference between paired observations Q 2 1-sample t-test compares one sample mean to a null hypothesis value. A paired t-test calculates the difference between multiple null hypotheses () They are the same exact things. just referred to as different tests depending on what types of samples are drawn from the populationIn a population, the birth rate and death rate are calculated as follows: Birth Rate = Number of birth I population Death Rate = Number of death I population for example, in a population of 100,000 that has 8,000 births and 6,000 deaths per year, the birth and death rate are: Birth Rate = 8,000 3' 100,000 2 0.08 Death Rate = 6,000 I 100,000 2 0.06 Design a Population class that stores. a population, number of birth, and number of deaths fora period ottime. Member function should return the birth rate and death rate. Implement the class in a program Input 1|u"alidation: Do not accept population figures less than 1, or birth or death number less then 0. (2.14) Drifting random walk. Random walks with a constant drift term will have a net correlation between steps. This prob- lem can be reduced to the problem without drift by shifting to a 'moving reference frame'. In par- ticular, suppose we have a random walk with steps independently drawn from a uniform den- sity p(() on [0,1), but with a non-zero mean (0) = 1#0. Argue that the sums s'N = En (en - () describe random walks in a moving reference frame, with zero mean. Argue that the variance of these ran- dom walks (the squared standard deviation ) is the same as the variance ((SN -SN)') of the original random walks.2. Random walk and stationarity. A random walk is expressed as X1 = Z1, Xt = Xt-1 + 7, t = 2,3,..., where Z ~ WN(uz, oz), that is, E(Z,) = uz, Var(Z,) = of, and Cov(Zt, Z,) = 0 for t # s. Determine which statements are true with respect to a random walk model; show calculations and provide complete explanations. I. If uz #0, then the random walk is nonstationary in the mean. ( Hint: Nonstationary in the mean means that the mean changes with time.) II. If of = 0, then the random walk is nonstationary in the variance. (Hint: Nonstationary in the variance means that the variance changes with time.) III. If of > 0, then the random walk is nonstationary in the variance