A poll reported that only 344 out of a total of 1507 adults in a particular region said they had a​ "great deal of​ confidence" or​ "quite a lot of​ confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Complete parts​ (a) through​ (d) below.

a. Find a 95​% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public​ schools, and interpret this interval.

The 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is Answer (_____ and _____)

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

We are Answer ____% confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between Answer (____ and ____)

B.. Find a 90​% confidence interval and interpret it.The 90​% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is

Answer (___, and ____) ​(Round to three decimal places as​ needed.)

Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice.

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

c. Find the width of each interval by subtracting the lower proportion from the upper​ proportion, and state which interval is wider. The width of the 95​% confidence interval is

Answer _____ and the width of the 90​% confidence interval is Answer _____ . The is wider.  (Round to three decimal places as​ needed.)

d. How would a 95% interval compare with the others in​ width? Answer _____ (A,B,C or D)

A. A 95​% interval would be narrower than the 99% confidence interval but wider than the 90​% confidence because intervals get wider with increasing confidence level.Your answer is correct.

B.A 95​% interval would be wider than the 99% confidence interval but narrower than the 90​% confidence because intervals get narrower with increasing confidence level.

C.A 95% interval would be wider than the 99​% confidence interval but narrower than the 90​% confidence because intervals get wider with increasing confidence level.

D.A 95% interval would be narrower than the 99​% confidence interval but wider than the 90% confidence because intervals get narrower with increasing confidence level.

Suppose y1, ... yn ~ iid N(0, sigma^2),

Ho: sigma = sigma0
Ha: sigma = sigma1.   where sigma0 < sigma1

Test rejects Ho when T(y) = Sum(yi^2) is large.

Find rejection region for the test for a specified level of alpha

Many boxed cake mixes include special high-altitude baking instructions. One would like to investigate that, on an average, cakes take longer to bake at high altitudes. A consumer group made several similar cakes in nine-inch rounded pans in Denver and Miami, and carefully recorded the time to bake (in minutes). The data is given as follows:

Baking Times at High Altitude 22.8 30.0 27.3 30.3 28.3 31.1 27.0 26.8 26.3 29.1 23.5 26.2 29.2 23.0

Baking Times at Low Altitude 25.1 25.6 24.9 23.7 25.5 22.4 24.7 24.2 25.6 24.8 23.9 24.4 24.7 24.4 26.4 24.7 24.7 26.8 24.9 24.3

(a)Draw side-by-side boxplots for low and high altitudes. Write a short description about what you observe from the boxplots by examining them individually and contrasting them with regard to measures of center, variability and shapes.

(b)Make a quantile-quantile plot of the data with a 45oline added to it. What does the plot tell you about the baking times at the low and high altitudes?

I cannot figure out the R-scripts to make the q-q plot. I need to know how to enter the data from excel into R for the plot. Thank you!!

The null, Ho, indicates that there is either no relationship or a positive relationship between Amazon’s growth over the past ten years and number of Best Buy brick and mortar locations.  The alternative, H1, seeks to prove that there is a negative relationship between the variables, Amazon and Best Buy brick and mortar locations. In other words, Amazon’s growth is negatively impacting Best Buy by forcing store location closures. Using a 95% confidence interval, construct a test of hypothesis using the following data:

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

H0: p=0.47 versus H1: p<0.47 n=150, x= 66, a=0.05

a) Is np0 (1-p0)> 10? b) What is the p-value? c) Should the hypothesis be rejected?

A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 19% were under 20 years old, 13% were in the 20- to 35-year-old bracket, 29% were between 36 and 50, 24% were between 51 and 65, and 15% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: Time ten years ago and today are independent.
H₁: Time ten years ago and today are not independent.

H₀: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are independent.
H₁: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are not independent.    

H₀: The distributions for the population 10 years ago and the population today are the same.
H₁: The distributions for the population 10 years ago and the population today are different.

H₀: The population 10 years ago and the population today are independent.
H₁: The population 10 years ago and the population today are not independent.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) 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

(iv) Conclude the test.

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 do not reject the null hypothesis.

Since the P-value < α, we do not reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that the age distribution of the population of Blue Valley has changed.

At the 1% level of significance, there is sufficient evidence to claim that the age distribution of the population of Blue Valley has changed.

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

(a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σx_i = 219.8.] (Round your answer to three decimal places.)
MPa


(b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%.
MPa


(c) Calculate a point estimate of the population standard deviation σ. [Hint: Σx_i² = 1863.16.] (Round your answer to three decimal places.)
MPa

(d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)


(e) Calculate a point estimate of the population coefficient of variation σ/μ. (Round your answer to four decimal places.)

In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded.

1. Use  = .05 and test the hypothesis that there is no difference in the recall proportions for the two commercials.
   
   Formulate the null and the alternative hypotheses.
   H₀: p₁ - p₂equal to 0
   H_a: p₁ - p₂not equal to 0
   
   What is the value of the test statistic (to 2 decimals)?
   
   
   What is the p-value (to 4 decimals)?
   
   
   Does there appear to be a difference in recall proportions for the two commercials?
   Yes
   
2. Compute a 95% confidence interval for the difference between the recall proportions for the two populations (to 4 decimals).
   (  ,   )
   
   

Linear Regression and Correlation.

Compute the equation of the linear regression line in the form y = mx + b, where m is the slope and b is the intercept.
Use at least 3 decimal places.
y =__x +___
Compute the correlation coeficient for this data set. Use at least 3 decimal places.
r=  

Compute the P-value (Use H_A: slope ≠ 0 for the alterantive hypothesis.)
P-value =  

At the alpha = 0.01 significance level, is the correlation significant?

• Yes, significant correlation
• No

Does 10K running time increase when the runner listens to music? Ten runners were timed as they ran a 10K with and without listening to music. The the running times in minutes are shown below.

Assume the distribution of the differences is normal. What can be concluded at the 0.01 level of significance? (d = Time Without music - Time With music)

a. H₀: μ_d = 0 H_a: μ_d 0

b. Test statistic (t or z):   =  Round to 2 decimal places,

c. p-Value =   Round your answer to 4 decimal places.

d. p-Value Interpretation: If the null hypothesis is  , then there is a  probability that the average of the sample differences is   (less than / more than)   (value to 2 decimal places) minutes.

e. Decision:   (Reject H₀ or do not Reject H₀)

f. Conclusion: There is  (sufficient / insufficient) evidence to make the conclusion that the population mean running time for a 10K   (increases / decreases) when the runners listen to music.

The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 48 male consumers was $135.67, and the average expenditure in a sample survey of 34 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $40, and the standard deviation for female consumers is assumed to be $23.

1. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
   67.03
2. At 99% confidence, what is the margin of error (to 2 decimals)?
   
3. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
   (  ,   )

a) Find the mode of the beta distribution

b) Find the mode of the gamma distribution

population 1 population 2

n 29 22

x 49.1 43.8

s 4.4 10.5

You just saw a commercial for the Tread Master, an exercise machine that claims an average weight loss of 10 pounds. A commercial for the Climber, a competing product, claims that only 1 out of 10 users of the Tread Master lost any weight at all. The rest of them gained weight. How can both of these claims be true?

A recent study of two vendors of desktop personal computers reported that out of 895 units sold by Brand A, 102 required repair, while out of 788 units sold by Brand B, 96 required repair. Round all numeric answers to 4 decimal places.

1. Calculate the difference in the sample proportion for the two brands of computers, ?̂??????−?̂??????p^BrandA−p^BrandB =  .

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands.

A. ?0:??−??=0H0:pA−pB=0, ??:??−??≠0HA:pA−pB≠0
B. ?0:??−??=0H0:pA−pB=0, ??:??−??<0HA:pA−pB<0
C. ?0:??−??=0H0:pA−pB=0, ??:??−??>0HA:pA−pB>0

3. Calculate the pooled estimate of the sample proportion, ?̂p^ =

4. Is the success-failure condition met for this scenario?

A. Yes
B. No

5. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

6. Calculate the p-value for this hypothesis test, p-value =  .

7. Based on the p-value, we have:
A. little evidence
B. very strong evidence
C. some evidence
D. strong evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

8. Compute a 95 % confidence interval for the difference ?̂??????−?̂??????p^BrandA−p^BrandB = (   ,  )