(PLEASE, SINCE THE VERY BEGINNING, ALL THE ONE BY ONE STEPS NEED TO BE MENTIONED IN YOUR CALCULATION) A manufacturer of cell phones guarantees that his cell phones will last, on average, 3 years with a standard deviation of 1 year. If 5 of those cell phones are found to have lifetimes of 1.9, 2.4, 3.0, 3.5 and 4.2 years, can the manufacturer still be convinced that his cell phones have a standard deviation of 1 year? Test at a 0.05 level of confidence. Thank you in advance for your help!

Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made the time period of January 1 to March 31. Table #11.2.4 gives the defect and the number of defects.

Table #11.2.4: Number of Defective Lenses

Do the data support the notion that each defect type occurs in the same proportion? Test at the 10% level.

The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.

Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are the same.
H₁: The distributions are the same.

H₀: The distributions are the same.
H₁: The distributions are different.    

H₀: The distributions are different.
H₁: The distributions are different.

H₀: The distributions are different.
H₁: The distributions are the same.

(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.)


Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

normal

Student's t    

binomial

uniform

chi-square

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 0.01 level of significance, the evidence is sufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site.

At the 0.01 level of significance, the evidence is insufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site.

Use the data in the file andy.dta consisting of data on hamburger franchises in 75 cities from Big Andy's Burger Barn.

Set up the model

ln(Si)=b1 + b2ln(Ai) + ei,

where

Si = Monthly sales revenue ($1000s) for the i-th firm

Ai = Expenditure on advertising ($1000s) for the i-th firm

(a) Interpret the estimates of slope and intercept.

(b) How well did the model fit to the data? Use any tests and measures presented in class.

(c) Perform any test for heteroscedasticity in your data.

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 31 women in rural Quebec gave a sample variance s² = 2.7. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ² = 5.1; H₁: σ² ≠ 5.1

H_o: σ² = 5.1; H₁: σ² < 5.1  

H_o: σ² < 5.1; H₁: σ² = 5.1

H_o: σ² = 5.1; H₁: σ² > 5.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a binomial population distribution.We assume a normal population distribution.    We assume a uniform population distribution.We assume a exponential population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.   

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1.

At the 5% level of significance, there is sufficient evidence to conclude that the that the variance of age at first marriage is less than 5.1.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 90% confident that σ² lies above this interval.

We are 90% confident that σ² lies within this interval.    

We are 90% confident that σ² lies below this interval.

We are 90% confident that σ² lies outside this interval.

1. A recent poll was conducted by the Gallup organization between April 2nd and April 8th, 2018. A total of 785 Facebook users living in the U.S. were selected using random digit dialing and were interviewed over the phone (either landline or cell phone). Respondents were asked the following question: “How concerned are you about invasion of privacy when using Facebook? Very concerned, somewhat concerned, not too concerned or not concerned.” 43% of those selected said “very concerned”. Suppose we want to study the proportion of all Facebook users who are “very concerned” about the invasion of privacy.

a) Define the parameter of interest in the context of the problem (include the symbol used to denote it).

b) What is the statistic in this problem (include the symbol used to denote it)?

c) Check the assumptions necessary to construct a normal-based confidence interval for the parameter of interest by verifying the appropriate conditions. Actually show that you checked these in the context of the problem.

d) Find the margin of error if we want 95% confidence in our estimate of the parameter of interest.

e) Find the 95% confidence interval for the parameter of interest.

f) In the context of the problem, give a conclusion based on the confidence interval you found in part e. Your sentence should start with the words “We are 95% confident that……”

Hi,

Im doing my final project for quanatative analysis class. I was tasked to create a regression analysis on Does the number of probowl player have bearing on becoming all pro. I ran the regression for the following data and got this output from Megastat but I'm not sure what it tells me.

The ideal (daytime) noise-level for hospitals is 45 decibels with a standard deviation of 9 db; which is to say, this may not be true. A simple random sample of 80 hospitals at a moment during the day gives a mean noise level of 47 db. Assume that the standard deviation of noise level for all hospitals is really 9 db. All answers to two places after the decimal.
(a) A 99% confidence interval for the actual mean noise level in hospitals is ( ___db, ___ db).
(b) We can be 90% confident that the actual mean noise level in hospitals is  db with a margin of error of ___ db.
(c) Unless our sample (of 81 hospitals) is among the most unusual 2% of samples, the actual mean noise level in hospitals is between ___ db and ___ db.
(d) A 99.9% confidence interval for the actual mean noise level in hospitals is (___ db, ___ db).
(e) Assuming our sample of hospitals is among the most typical half of such samples, the actual mean noise level in hospitals is between ___ db and ___db.
(f) We are 95% confident that the actual mean noise level in hospitals is  db, with a margin of error of ___db.
(g) How many hospitals must we examine to have 95% confidence that we have the margin of error to within 0.25 db?
(h) How many hospitals must we examine to have 99.9% confidence that we have the margin of error to within 0.25 db?

According to a genetic model, the distribution of fur color of the second generation Havana rabbit (Oryctolagus cuniculus) should be 1:2:1, black:gray:brown. In a sample of second generation rabbits, there are 10 black, 27 gray, and 16 brown rabbits. Assuming random sample and independent observations, does this sample of rabbits suggest that the actual fur color distribution differs from the genetic model? Include all steps for full credit.

Assuming the sample represents the population very well, that is, the population has approximately the same mean and same standard deviation.

a) 68% of the population fall between ___ inches and ___ inches

b) 95% of the population fall between ___ inches and ___ inches

c) 99.7% of the population fall between ___ inches and ___ inches

Please answer (F)

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 31 women in rural Quebec gave a sample variance s² = 2.7. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 5.1; H₁: σ² ≠ 5.1H_o: σ² = 5.1; H₁: σ² < 5.1    H_o: σ² < 5.1; H₁: σ² = 5.1H_o: σ² = 5.1; H₁: σ² > 5.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a binomial population distribution.We assume a normal population distribution.    We assume a uniform population distribution.We assume a exponential population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1.

At the 5% level of significance, there is sufficient evidence to conclude that the that the variance of age at first marriage is less than 5.1.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 90% confident that σ² lies above this interval.

We are 90% confident that σ² lies within this interval.

We are 90% confident that σ² lies below this interval.

We are 90% confident that σ² lies outside this interval.

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 90 words per minute​ (wpm) and a standard deviation of 10 wpm. Complete parts​ (a) through​ (f).

​(a) What is the probability a randomly selected student in the city will read more than 95 words per​ minute?

​(b) What is the probability that a random sample of 13 second grade students from the city results in a mean reading rate of more than 95 words per​ minute? then interpret this probability.

(c) What is the probability that a random sample of 26 second grade students from the city results in a mean reading rate of more than 95 words per​ minute? then interpret.

(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result.

(e) 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 92.3 wpm. What might you conclude based on this​ result? Select the correct choice below and fill in the answer boxes within your choice.

(f) There is a​ 5% chance that the mean reading speed of a random sample of 24 second grade students will exceed what​ value?

Yellow stains on white clothing are stubborn discolorations believed to result from oxidated body oils that have reacted chemically with clothing’s cellulose fibers (as if it were a dye). In as little as one week, there reaction can permanently discolor with clothing with an ugly yellow stain and at this point the most potent laundry product will usually be of little value in removing them. Suppose researchers at the Department of Textiles and Apparel at Cornell University, experimenting with new experimental formulations to remove stains, washed six discolored strips in each of three experimental formulations, and the results as follows Coloring rating (after washing) 0 = Dark Yellow, the initial shade 20 = Pure White-All washed strips were matched to a color chart, a series of increasingly lighter shade, and rated from 0 to 20. Formulation X Y Z 10 8 11 9 10 12 10 12 14 12 9 11 8 10 10 11 8 14 Three Different Formulations were tested a) Calculate by hand the average color rating and variance for each group b) Assuming valid random samples, test at 5% level significance whether differences among the three-sample means can be attributed to chance fluctuation or, indeed, to actual differences in the stain-eliminating ability of the three formulations. ( hint: find the F-ratio) c) Briefly discuss the implications of these results. Need to solve by hand. Please help!

A research council wants to estimate the mean length of time (in minutes) that the average U.S. adult spends watching television using digital video recorders (DVR’s) each day. To determine the estimate, the research council takes random samples of 35 U.S. adults and obtains the following times in minutes.

From past studies, the research council has found that the standard deviation time is 4.3 minutes and that the population of times is normally distributed.

Construct a 90% confidence interval for the population mean.

Construct a 99% confidence interval for the population mean.

Interpret the results and compare the widths of the confidence intervals.

Test the claim that the mean time spent watching DVR’s is 20 minutes each day using a significance level of 0.05.

You may use Stat Disk, TI-84 calculator, or CrunchIt to find the confidence intervals. Be sure to show your results in your post.

(3) A random sample of 51 fatal crashes in 2009 in which the driver had a positive blood alcohol concentration (BAC) from the National Highway Traffic Safety Administration results in a mean BAC of 0.167 grams per deciliter (g/dL) with a standard deviation of 0.010 g/dL.

(a) What is a point estimate for the mean BAC of all fatal crashes with a positive BAC?

(b) In 2009, there were approximately 25,000 fatal crashes in which the driver had a positive BAC. Explain why this, along with the fact that the data were obtained using a simple random sample, satisfies the requirements for constructing a confidence interval.

(c) Determine and interpret a 98% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC. Do not use the T-Interval or Z-Interval features of your calculator.