A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1064 people age 15 or​ older, the mean amount of time spent eating or drinking per day is 1.28 hours with a standard deviation of 0.75 hour.

Determine and interpret a 99​% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.

Let Y ₁ ,...,Y _n be a sample from the density f(y) = λ ² ye ^−λy , y > 0 where λ > 0 is an
unknown parameter.
(a) Find an estimator 'λ ₁ of λ by Method of Moments
(b) Find an estimator 'λ ₂ of λ by Method of Maximum Likelihood.
(c) Find an estimator 'λ ₃ of λ that is a Sufficient estimator. Can you construct a
Minimal Variance Unbiased Estimator? Justify.

Suppose that Y₁ ,Y₂ ,...,Y_n is a random sample from distribution Uniform[0,2].

Let Y_(n) and Y₍₁₎ be the order statistics.
(a) Find E(Y₍₁₎)
(b) Find the density of (Y_(n) − 1)²
(c) Find the density of Y_(n) − Y ₍₁₎

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfill each week is 2. (a) What is the probability that in a given week the plant cannot fulfill all the placed orders? (b)Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

The level of various substances in the blood of kidney dialysis patients is of concern because kidney failure and dialysis can lead to nutritional problems. A researcher performed blood tests on several dialysis patients on 6 consecutive clinic visits. One variable measured was the level of phosphate in the blood. Phosphate levels for an individual tend to vary normally over time. The data on one patient, in milligrams of phosphate per deciliter (mg/dl) of blood, are given below.

(a) Calculate the sample mean x and its standard error.
x =  

S_x =

(b) Use the t procedures to find the margin of error for a 90% confidence interval for this patient's mean phosphate level.
margin of error =  

(c) Use the t procedures to give a 90% confidence interval for this patient's mean phosphate level.
90% CI = (______ , _______ )

A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 35.2 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, do you support or reject the organization’s claim using the test statistic?

There are two ways for a concrete truck to go from a ready-mixed concrete plant to the construction site. The first way is direct, for which the mean and standard deviation of travel time are 30 min and 5 min, respectively. The second way is through Town A. The mean and standard deviation of travel time between the plant and Town A are 14 min and 5 min, respectively. The mean and standard deviation of travel time between Town A and the construction site are 14 min and 6 min, respectively. If the total travel time is above 45 min, the concrete in the truck will go bad. Calculate the probability that the concrete goes bad for both cases of choosing the direct and indirect ways. Assume travel time has a normal distribution.

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago x̄ 82 88 σ2 112.5 54 n 45 36

The 95% confidence interval for the difference between the two population means is

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfill each week is 2. (a) What is the probability that in a given week the plant cannot fulfill all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

A financial planner tracks the number of new customers added each quarter for a 6 year period. The data is presented below:

Year               Quarter                      New                Year               Quarter          New

2014               I                                   31                    2017               I                       69

                        II                                  24                                            II                      54

                        III                                 23                                            III                     46

                        IV                                16                                            IV                    32

2015               I                                   42                    2018               I                       82

                        II                                  35                                            II                      66

                        III                                 30                                            III                     51

                        IV                                23                                            IV                    38

2016               I                                   53                    2019               I                       91

                        II                                  45                                            II                      72

                        III                                 39                                            III                     59

                        IV                                27                                            IV                    41

Create a simple linear trend regression model. Let t=0 in 2013: IV. This is a computer deliverable.

(a) Interpret the slope coefficient.

(b) Test to see if the number of new customers is increasing over time. Use alpha = 0.01.

(c) Test to see if the model has explanatory power. Use alpha = 0.05.

(d) Forecast the number of new customers in the first and second quarters of 2020.

Create a multiple regression equation incorporating both a trend (t=0 in 2013: IV) and dummy variables for the quarters. Let the first quarter represent the reference (or base) group. Complete (e) thru (h) using your results. This is a computer deliverable.

(e) Test to see if there is an upward trend in new customers. Use alpha = 0.01.

(f) Test to see if the model has explanatory power. Use alpha = 0.05.

(g) Forecast the number of new customers in the first and second quarters of 2020.

(h) Test for the existence of first order autocorrelation, use alpha = 0.05. The calculated dw = 1.19.

Consider the data.

(a)

Compute the mean square error using equation  s² = MSE =

 . (Round your answer to two decimal places.)

(b)

Compute the standard error of the estimate using equation s =

=

 . (Round your answer to three decimal places.)

(c)

Compute the estimated standard deviation of

b₁

using equation s_b1 =

. (Round your answer to three decimal places.)

(d)

Use the t test to test the following hypotheses (α = 0.05):

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. We cannot conclude that the relationship between x and y is significant. Reject H₀. We conclude that the relationship between x and y is significant.      Do not reject H₀. We cannot conclude that the relationship between x and y is significant. Do not reject H₀. We conclude that the relationship between x and y is significant.

(e)

Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.

Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.)

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that the relationship between x and y is significant. Reject H₀. We conclude that the relationship between x and y is significant.      Do not reject H₀. We conclude that the relationship between x and y is significant.Reject H₀. We cannot conclude that the relationship between x and y is significant.

Assume that two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.

A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 14 cans of type B were selected and applied to similar surfaces. The​ drying​ times,​ in​ hours, were recorded. The summary statistics are below.

Type​ A:  

x overbar 1 equals 75.7x1 = 75.7

hours​,

s 1 equals 4.5s1 = 4.5

​hours, n 1 equals 11n1 = 11Type​ B:

x overbar 2 equals 72.7x2 = 72.7

hours​,

s 2 equals 4.7s2 = 4.7

​hours, n 2 equals 14n2 = 14

Test the claim that there is a difference between the mean drying times of the two types of paint.

Give the​ p-value. Round to four decimal places.

A teacher instituted a new reading program at school. After 10 weeks in the​ program, it was found that the mean reading speed of a random sample of 20 second grade students was

94.4 wpm. What might you conclude based on this​ result? Select the correct choice below and fill in the answer boxes within your choice.

​(Type integers or decimals rounded to four decimal places as​ needed.)

A. A mean reading rate of 94.4 wpm is not unusual since the probability of obtaining a result of 94.4 wpm or more is ____. This means that we would expect a mean reading rate of 94.4

or higher from a population whose mean reading rate is 92 in ____ of every 100 random samples of size n=20 students. The new program is not abundantly more effective than the old program.

B. A mean reading rate of 94.4 wpm is unusual since the probability of obtaining a result of 94.4 wpm or more is ____. This means that we would expect a mean reading rate of 94.4

or higher from a population whose mean reading rate is 92 in ____ of every 100 random samples of size n=20 students. The new program is abundantly more effective than the old program.

Can the standard error be a negative (no. 8). Is it possible to check the others

For each of the following, circle your answer to indicate whether the quantity can NEVER be negative or can SOMETIMES be negative:

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $19 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μx = 19 and standard error σx = $1.11.

The sampling distribution of x is approximately normal with mean μx = 19 and standard error σx = $7.

The sampling distribution of x is approximately normal with mean μx = 19 and standard error σx = $0.18.

The sampling distribution of x is not normal.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is not necessary to make any assumption about the x distribution because n is large.

It is necessary to assume that x has a large distribution.

It is not necessary to make any assumption about the x distribution because μ is large.

It is necessary to assume that x has an approximately normal distribution.

(b) What is the probability that x is between $17 and $21? (Round your answer to four decimal places.)

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $17 and $21? (Round your answer to four decimal places.)

(d) In part (b), we used x, the average amount spent, computed for 40 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The mean is larger for the x distribution than it is for the x distribution.

The standard deviation is smaller for the x distribution than it is for the x distribution.

The x distribution is approximately normal while the x distribution is not normal.

The sample size is smaller for the x distribution than it is for the x distribution.

The standard deviation is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.

The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.