Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale ( 1=1= 1 equals extremely unpleasing, 7=7= 7 equals extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data stored in Coffee contain the ratings accumulated over all four characteristics:

• a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands?

• b. What assumption is necessary about the population distribution in order to perform this test?

• c. Determine the p-value in (a) and interpret its meaning.

• d. Construct and interpret a 95% confidence interval estimate of the difference in the mean ratings between the two brands.

SHOW EXCEL FUNCTIONS USED TO ANSWER.

Isabella gathered data on the average percentage of tips received by waitstaff in 31 restaurants in New York City. She works through the testing procedure:

• H0:μ=14%; Ha:μ≠14%
  
• α=0.1 (significance level)
  
• The test statistic is t0=x¯−μ0sn√=1.489.
  
• The critical values are ±t0.05=±1.697.
  

Conclude whether to reject or not reject H0. Select two responses below.

Select all that apply:

• Reject H0.

• Fail to reject H0.

• The test statistic falls within the rejection region.

• The test statistic is not in the rejection region.

2. Set up both the vector of state probabilities and the matrix of transition probabilities given the following information: Store 1 currently has 40% of the market; store 2 currently has 60% of the market. In each period, store 1 customers have an 80% chance of returning; 20% of switching to store 2.

In each period, store 2 customers have a 90% chance of returning; 10% of switching to store 1. a.

Find the percentage of market for each store after 2 periods. b. Find the equilibrium conditions of 2 stores (limiting probabilities). What’s the meaning of these probabilities?

A study of the career paths of hotel general managers sent questionnaires to an SRS of 240 hotels belonging to major U.S. hotel chains. There were 133 responses. The average time these 133 general managers had spent with their current company was 12.37 years. (Take it as known that the standard deviation of time with the company for all general managers is 1.5 years.) (a) Find the margin of error for a 90% confidence interval to estimate the mean time a general manager had spent with their current company: years (b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: years (c) In general, increasing the confidence level the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)

A) estimate the error in the values of the gaussian approximation of the binomial coefficients g(12,2s) as 2s changes from 0 to its maximum value. (N=12 2s between states)

B) How will the error in the value g(N,0) calculated using the gausian approximation in A if you use N=20?

Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator wants to test whether children with chronic bronchitis have restricted PEF. A sample of 40 children with chronic bronchitis is studied, and their mean PEF is 279 with a standard deviation of 71. Is there statistical evidence of a lower mean PEF in children with chronic bronchitis? (α = 0.05, enter 1 for “yes”, and 0 for “no”).

A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly

16%

of all applications were from minority members, and exactly

14%

of the

2100

open positions were filled by members of the minority.

1. Find the mean of

   p

   , where

   p

   is the proportion of minority member applications in a random sample of

   2100

   that is drawn from all applications.
2. Find the standard deviation of

   p

   .
3. Compute an approximation for

   P≤p0.14

   , which is the probability that there will be

   14%

   or fewer minority member applications in a random sample of

   2100

   drawn from all applications. Round your answer to four decimal places.

1. Given a two-tailed test with test statistic a = 1.62 and n = 0.10, find the the p-value and determine if we reject or fail to reject ho. Say why

2. In a recent survey of parents at Clairmont Elementary, 51 out of 75 parents supported including sign language as a part of the elementary school curriculum. In a survey of Minnesota elementary schools, it was published that 56% of parents support including sign language in elementary school curriculum. At a 5% level of significance, are Clairmont Elementary’s results the same as the state percentage? Conduct a seven-step hypothesis test.

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Do you try to pad an insurance claim to cover your deductible? About 45% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 126 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.)

(a) half or more of the claims have been padded


(b) fewer than 45 of the claims have been padded


(c) from 40 to 64 of the claims have been padded


(d) more than 80 of the claims have not been padded

A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers and stored in Bank1. These data are:

Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 p.m. lunch period. Data are collected from a random sample of 15 customers and stored in Bank2. These data are:

• a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? (Use α=0.05.α=0.05. alpha equals , 0.05.)

• b. Determine the p-value in (a) and interpret its meaning.

• c. In addition to equal variances, what other assumption is necessary in (a)?

• d. Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches.

SHOW EXCEL FUNCTIONS USED TO ANSWER.

The amount of water in a bottle is approximately normally distributed with a mean of 2.40 liters with a standard deviation of 0.045 liter. Complete parts​ (a) through​ (e) below. a).What is the probability that an individual bottle contains less than 2.36 ​liters? b). If a sample of 4 bottles is​ selected, what is the probability that the sample mean amount contained is less than 2.36 ​liters? c).If a sample of 25 bottles is​ selected, what is the probability that the sample mean amount contained is less than 2.36 ​liters? d.) Explain the difference in the results of​ (a) and​ (c). Part​ (a) refers to an individual​ bottle, which can be thought of as a sample with sample size .1875 nothing. ​Therefore, the standard error of the mean for an individual bottle is 01 nothing times the standard error of the sample in​ (c) with sample size 25. This leads to a probability in part​ (a) that is ▼ the probability in part​ (c).

Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $130,000. This distribution follows the normal distribution with a standard deviation of $39,000.

a) If we select a random sample of 68 households, what is the standard error of the mean?

Standard Error of the Mean:

b) What is the expected shape of the distribution of the sample mean?

The distribution will be:

c) What is the likelihood of selecting a sample with a mean of at least $135,000?

Probability:

d) What is the likelihood of selecting a sample with a mean of more than $121,000?

Probability:

e) Find the likelihood of selecting a sample with a mean of more than $121,000 but less than $135,000.

Probability:

Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: 114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93 These 31 girls are an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be σ = 15. We expect the distribution of IQ scores to be close to Normal. Estimate the mean IQ score for all seventh-grade girls in the school district, using a 96% confidence interval. to

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 10 feet per year and σ = 3.7 feet per year.

Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.)

(a) an escape dune will move a total distance of more than 90 feet in 9 years

(b) an escape dune will move a total distance of less than 80 feet in 9 years

(c) an escape dune will move a total distance of between 80 and 90 feet in 9 years