Bags of whole coffee beans are filled automatically on a production line. A machine fills each bag so that the weight of coffee beans inside is normally distributed with a mean of 290 grams. The label on the bag, however, states that the weight of coffee beans inside is 283 grams.

a. What is the standard deviation of bags of coffee beans, if 13% of the bags have a weight below what is stated on the label?

b. New management wants to be more accurate to their customers and reduce the number of bags that are sent out under the weight of 283 grams listed on the label. They set a goal of sending no more than 1% of bags of coffee that are under the weight of 283 grams. To do this, the management ordered a new filling machine which decreased the standard deviation to 2.3151 grams. The weight of the bags of coffee beans will still be normally distributed. To what mean weight should the new equipment be set, with this new standard deviation and to meet their goal? The machine may only take a one decimal approximation.

Consider the following hypotheses:

H₀: p ≥ 0.48

H_A: p < 0.48

Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1057 and a standard deviation of 203. Scores on the ACT test are normally distributed with a mean of 22.6 and a standard deviation of 4.9. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 34-percentile, find the actual SAT score.
SAT score =  
Round answer to a whole number.

What would be the equivalent ACT score for this student?
ACT score =  
Round answer to 1 decimal place.

If a student gets an SAT score of 1341, find the equivalent ACT score.
ACT score =  
Round answer to 1 decimal place.

A large​ family-held department store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 40 complaints that were made in the last year. Use the data to complete parts​ (a) through​ (d) below.

Click the icon to view the data table.

a. Construct a

9595​%

confidence interval estimate for the population mean number of days between the receipt of a complaint and the resolution of the complaint.The

9595​%

confidence interval estimate is from

28.728.7

days to

51.451.4

days.

​(Round to one decimal place as​ needed.)

b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in​ (a)?

A.

The number of complaints per day is normally distributed.

B.

The number of days to resolve complaints follows the t distribution.

C.

The number of days to resolve complaints is normally distributed.

Your answer is correct.

D.

The number of complaints per day follows the t distribution.

c. Do you think that the assumption needed in order to construct the confidence interval estimate in​ (a) is​ valid? Explain.

A.

​No, the data suggest the population distribution is skewed to the right.

This is the correct answer.

B.

​Yes, the data suggest the population distribution approximately follows the t distribution.

C.

​Yes, the data suggest the population distribution is approximately normal.

Your answer is not correct.

D.

​No, the data suggest the population distribution is skewed to the left.

d. What effect might your conclusion in​ (c) have on the validity of the results in​ (a)?

ai) Find the mean number of claims made by the sample of smokers and nonsmokers in the group separately.(i.e mean of smokers, mean of nonsmokers)

ii) What is the standard deviation of family size for this population of workers? (standard deviation of popuation) Standardize by converting your “X” values into “Z” values to see whether their historical values match up well with the new company. Use a Z table Hint: use the (ai) and (aii) values along with the means and standard deviations you calculated.

b) First find the Z-value for smokers.

c) And now the Z for nonsmokers.

d) Using your Z-table, find the probability that a nonsmoker will make fewer than 6 claims.

e) Next, find the probability that a smoker will make more than 11 claims.

f) Final Recommendation: This firm will be more risky than the current customer risk pool. True or False

7. In an area of the Great Plains, records were kept
on the relationship between the rainfall (in inches)
and the yield of wheat (bushels per acre).

7a. Using the linear
regression feature on your calculator,
find a linear equation that models the
miles per gallon as the respone
variable (y) and the engine size in
liters as the explanatory variable (x). (Use 2 decimal places in the regression equation.)

7b. Using the line you obtained in 7a. above, compute the sum of the squared
residuals of the least squares line for the given data. (Use 2 decimal places and show your
calculations, by hand!)

Jobs are sent to a server at a rate of 2 jobs per minute. We will model job arrivals using a (homogenous) Poisson process. For each question, clearly specify the parameter value(s) of the distribution as well as its name. (a) What is the probability of receiving more than 3 jobs in a period of one minute? (b) What is the probability of receiving more than 30 jobs in a period of 10 minutes? (No need to simplify.) (c) What is the expected value and the variance of inter-arrival times? (d) Compute the probability that the next job does not arrive during the next 30 seconds. (e) Compute the probability that the time till the fourth job arrives exceeds 40 seconds.

Twenty percent of the contestants in a scholarship competition come from Pylesville High School, 40% come from Millerville High School, and the remaining come from Lakeside High School. Two percent of the Pylesville students are among the scholarship winners; 3% of the Millerville contestants and 5% of the Lakeside contestants win. a) If a winner is chosen at random, what is the probability that they are from Lakeside? b) What percentage of the winners are from Pylesville?

How are exploratory data analysis (EDA) and hypothesis testing different? Explain why EDA could be preferred in data mining, and justify your explanation with a specific example.

The scores of the top ten finishers in a recent Buick Open are listed below: Scores 65 66 67 66 67 67 70 71 68 70 Round all solutions one decimal place. You must show ALL of your work to receive credit for these problems. e) Find the variance of the data. f) Find the standard deviation of the data. g) Find quartile one, Q1 , of the data. Interpret the first quartile in the context of the problem. h) Find quartile three, Q 3 , of the data. Interpret the third quartile in the context of the problem. i) Find the inter-quartile range, IQR, of the data. Interpret the IQR in the context of the problem. j) List the Five Number Summary. k) Construct a Box-and-Whisker Plot for the data set. (Don’t forget the title)

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1389 referee​ calls, with the result that 427 of the calls were overturned. Women challenged 779 referee​ calls, and 227 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis​ test? A. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1not equalsp 2 Your answer is correct.B. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1less thanp 2 C. Upper H 0​: p 1less than or equalsp 2 Upper H 1​: p 1not equalsp 2 D. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1greater thanp 2 E. Upper H 0​: p 1not equalsp 2 Upper H 1​: p 1equalsp 2 F. Upper H 0​: p 1greater than or equalsp 2 Upper H 1​: p 1not equalsp 2 Identify the test statistic. zequals .78 . 78 ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals .782218435 . 435 ​(Round to three decimal places as​ needed.) What is the conclusion based on the hypothesis​ test? The​ P-value is greater than the significance level of alphaequals0.01​, so fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls. b. Test the claim by constructing an appropriate confidence interval. The 99​% confidence interval is -.199 negative . 199less thanleft parenthesis p 1 minus p 2 right parenthesisless than -.200 negative . 200. ​(Round to three decimal places as​ needed.)

Joe, Ken and Ben, they live in a shared house. Each Sunday each of the tenants choose uniformly at random and independence of other tenant one part of the house: kitchen(K), living room(L),bathroom(B),garage(G). and cleans it during the week that follows( here week means a period of 7 days starting on Sunday)

(a) what is the probability that the garage is not cleaned during one week?

(b) what is the probability that the kitchen is cleaned exactly once during one week?

Assume that you have a sample of

n 1 equals 8n1=8​,

with the sample mean

Upper X overbar 1 equals 48X1=48​,

and a sample standard deviation of

Upper S 1 equals 4 commaS1=4,

and you have an independent sample of

n 2 equals 12n2=12

from another population with a sample mean of

Upper X overbar 2 equals 35X2=35

and the sample standard deviation

Upper S 2 equals 7.S2=7.

Complete parts​ (a) through​ (d) below.

What is the value of the​ pooled-variance t Subscript STATtSTAT test statistic for testing Upper H 0 : mu 1 equals mu 2H0: μ1=μ2​?, In finding the critical​ value, how many degrees of freedom are​ there?, Using a significance level of alpha α equals=0.250.25​, what is the critical value for a​ one-tail test of the hypothesis, Upper H 0 : mu 1 less than or equals mu 2H0: μ1≤ μ2 against the alternative Upper H 1 : mu 1 greater than mu 2 question mark, What is your statistical​ decision?

1. State the hypothesis and identify the claim.

H0:

H1:

2. Find the critical value and determine what error level to use. For all the problems on this homework use an alpha level of .05 Determine if the test is right tailed, left tailed or non-directional.
3. Compute the test Value It will be an ANOVA,
4. Make a decision to reject or fail to reject the null hypothesis.
5. Summarize the results

Problem #2 You are a researcher who wants to know if there is a difference in the means of three different groups you have been working with to stop smoking. You have randomly selected 15 smokers and randomly placed them into three groups. Group one receives traditional treatment, pamphlets and videos on the health risks of smoking. Group two receives a fake treatment in the form of a daily pill, this is a placebo. The third group will receive motivational interviewing treatment within their weekly counseling sessions. All smokers in the three groups smoke on average 20 cigarettes a day. You hypothesize that there will be some difference between the three groups or within the three groups. Using an alpha level of .05, use the five-step approach to reject or fail to reject the HO: that all three groups will have equal means. Remember to report the P value as well. Critical values to determine the critical region can be found using table H on page 654. You must find the degrees of freedom for the numerator and the denominator. The following data shows how many cigarettes group participants smoked after eight weeks of treatment.

Group 1       Group 2       Group 3

20                 18                6

18                 20                3

21                 23                1

17                19                2

19                 18                1

Bonus Points 10. Must answer all possibilities to receive points. What are the independent variables and what is the dependent variable?

Suppose a simple random sample of size n equals=1000 is obtained from a population whose size is N equals=1,000,000 and whose population proportion with a specified characteristic is p=0.74.

​(b) What is the probability of obtaining x=770 or more individuals with the​ characteristic?

​(c) What is the probability of obtaining x=720 or fewer individuals with the​ characteristic?

​(Round to four decimal places as​ needed.)

How to solve these problems in Statcrunch? Thank you!