A hospital administrator has been asked by her supervisor to assess whether waiting time in the emergency room (ER) has changed from last year, when average wait time was 127 minutes. The administrator collects a simple random sample of 64 patients and records the time between when they checked in at the ER until they were first seen by a doctor; the average wait time is 137 minutes, with standard deviation 39 minutes.

a) Compute and interpret a 95% confidence interval for mean ER wait time at the hospital. Based on the interval, is mean ER wait time statistically significantly different from 127 minutes at the α = 0.05 level?

2. b) Would the conclusion in part a) change if the significance level were changed to α = 0.01?

3. c) Suppose that upon seeing the results from part a), the supervisor criticizes the hospital administrator on the basis that ER wait times have increased greatly from last year and the administrator must be at fault. Present a brief argument in favor of the administrator.

Puppies were sorted into three groups, based upon which food they preferred when given a choice: Brand A puppy food, Brand B puppy food, or a diet of cooked ground meat. For two months, each group was restricted to its preferred diet (they were no longer given a choice in diet). Measurements for the height, weight, and length of the puppies was taken each week for two months. The puppies in the group with the diet of cooked ground meat had significantly more growth than the other two groups.

What conclusion can be drawn from this study?

A. There is a causal relationship between diet and puppy growth.

B. No conclusions can be made because there was not a group that received a placebo.

C. It is not possible to make any conclusions because there could be lurking variables that were not considered that caused the difference in growth.

D. There is clear evidence of an association between diet and puppy growth, but it cannot be said there is a causal relationship between diet and puppy growth.

I know the answer is D, my question is why?

Psychologists question the importance of biodiversity on the psychological health of humans in urban areas. Urban residents often visit green spaces such as parks within urban environments. Fuller et al., conducted a study on 15 different green spaces to determine the impacts of green space on people's psychological health.

To assess how much people liked the green space, scientists had participants fill out a survey to determine their attachment to the green space. Scientists then then quantified the biodiversity of birds, plants, and butterflies at the different green spaces.

Here is a link to a dataset relating biodiversity to residents' attachment to a location.

Which biodiversity measurement (butterfly species; bird species; plant species) variable is most strongly correlated with residents' "attachment"?  

Calculate the correlation coefficients using the =correl() function in Excel.

What is the standard error of that correlation?  

Calculate your answer using Excel and report your answer to four decimal places.

Which species exhibited the weakest correlation?  

What is the correlation coefficient of the weakest relationship?  

Calculate your answer using Excel and report your answer to four decimal places.

What is the value of t for the correlation of bird species?

Report your answer to four decimal places

What is the p value associated with the t value calculated in Question 5? Use the excel formula =2*(1-(T.Dist(ABS(t,df,TRUE))))

This is a two-tailed t-test

degrees of freedom (df) = n - 2

We are using a cumulative probability function so we type TRUE

Report your answer to 4 decimal places

Based on this p value, should the authors reject or fail to reject the null hypothesis that bird species abundance is not correlated to attachment?

DATA SET

I am starting my first statistics and probability course at my university. What is the best way to study this subject and get good grades?

Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used 180 pounds as a typical passenger weight (including carry-on luggage) in warm months and 185 pounds as a typical weight in cold months.

A journal reported that an airline conducted a study to estimate average passenger plus carry-on weights. They found an average summer weight of 183 pounds and a winter average of 190 pounds. Suppose that each of these estimates was based on a random sample of 100 passengers and that the sample standard deviations were 18 pounds for the summer weights and 25 pounds for the winter weights.

(a)

Construct a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers. (Round your answers to three decimal places.)

Interpret a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers.

There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is one of these two values. There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values.     We are 95% confident that the true mean summer weight (including carry-on luggage) of this airline's passengers is between these two values. There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is between these two values. We are 95% confident that the true mean summer weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values.

(b)

Construct a 95% confidence interval for the mean winter weight (including carry-on luggage) of this airline's passengers. (Round your answers to three decimal places.)

Interpret a 95% confidence interval for the mean winter weight (including carry-on luggage) of this airline's passengers.

There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is one of these two values. There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values.     We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values. There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values. We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values.

(c)

The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from part (a) and part (b).

Only the new winter FAA recommendation seems accurate, since only the new winter recommendation value is contained within its 95% confidence interval. Only the new summer FAA recommendation seems accurate, since only the new summer recommendation value is contained within its 95% confidence interval.     These new FAA recommendations don't seem accurate, since neither recommendation value is contained within its respective 95% confidence interval. These new FAA recommendations seem accurate, since both recommendation values are contained within their respective 95% confidence interval.

You may need to use the appropriate table in Appendix A to answer this question.

The number of undergraduate students at the University of Winnipeg is approximately 9,000, while the University of Manitoba has approximately 27,000 undergraduate students. Suppose that, at each university, a simple random sample of 3% of the undergraduate students is selected and the following question is asked: “Do you approve of the provincial government’s decision to lift the tuition freeze?”. Suppose that, within each university, approximately 20% of undergraduate students favour this decision. What can be said about the sampling variability associated with the two sample proportions?
(A) The sample proportion for the U of W has less sampling variability than that for the U of M.

(B) The sample proportion for the U of W has more sampling variability that that for the U of M.

(C) The sample proportion for the U of W has approximately the same sampling variability as that for the U of M.

(D) It is impossible to make any statements about the sampling variability of the two sample proportions without taking many samples.

(E) It is impossible to make any statements about the sampling variability of the two sample proportions because the population sizes are different.

Could you explain why answer is (B)

What business, economic, policy, and environmental threats to organization growth are CEOs extremely concerned about? In a survey by PricewaterhouseCoopers (PwC), 57 of 114 U.S. CEOs are extremely concerned about cyber threats, and 22 are extremely concerned about lack of trust in business.

a. Construct a 95% confidence interval estimate for the population proportion of U.S. CEOs who are extremely concerned about cyber threats.

b. Construct a 95% confidence interval estimate for the population proportion of U.S. CEOs who are extremely concerned about lack of trust in business.

c. Interpret the intervals in (a) and (b).

let v and u are random variables fvu(v,u)= e^-v-u for u ,v>=0 Z= e^v+u find fz(z) ?

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 15.7 years and a standard deviation of 1.2 years.

Find the probability that a randomly selected quartz time piece will have a replacement time less than 13.4 years?
P(X < 13.4 years) =

Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If the company wants to provide a warranty so that only 1.5% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
warranty =   years

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A certain flight arrives on time

8383

percent of the time. Suppose

147147

flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly

128128

flights are on time.​(b) at least

128128

flights are on time.​(c) fewer than

127127

flights are on time.​(d) between

127127

and

132132​,

inclusive are on time.

A company that produces coffee for use in commercial machines monitors the caffeine content in its coffee. The company selects 35 8-oz samples each hour from its production line to analyze. The samples collected one morning between 8:00 - 9:00 am contained on average 96.1 mg of caffeine, with standard deviation 1.2 mg.

1. a) Compute and interpret a 95% confidence interval for mean caffeine content based on the collected data.

2. b) According to production standards, the mean amount of caffeine content per 8 ounces should be no more than 95 mg. An overly high caffeine content indicates that the coffee beans have not been roasted long enough.

   Conduct a formal hypothesis test to investigate whether production standards are being met, based on the observed data. Summarize your findings to the CEO using language accessible to someone who has not taken a statistics course and make a recommendation as to whether an adjustment needs to be made to the bean roasting time.

3. c) A set of samples collected between 10:00 - 11:00 am on the same day has average caffeine content of 95.3 mg, with standard deviation 1.1 mg. Based on observing this data, would you change your recommendation in part c)? Explain your answer.

(A derivation of the bivariate normal distribution) let $Z_{1}$ and $Z_{2}$ be independent n(0,1) random variables, and define new random variables X and Y by\\
\begin{align*}
X=a_{x}Z_{1}+b_{x}Z_{2}+c_{x} \quad Y=a_{Y}Z_{1}+b_{Y}Z_{2}+c_{Y}\\
\end{align*}
where $a_{x},b_{x},c_{x},a_{Y},b_{Y},c_{Y}$ are constants.\\
if we define the constants $a_{x},b_{x},c_{x},a_{Y},b_{Y},c_{Y}$ by\\
\begin{align*}
a_{x}=\sqrt{\frac{1+\rho}{2}}\sigma_{X}, b_{x}=\sqrt{\frac{1-\rho}{2}}\sigma_{X}, c_{X}=\mu_{X},\\
a_{Y}=\sqrt{\frac{1+\rho}{2}}\sigma_{Y}, b_{Y}=-\sqrt{\frac{1-\rho}{2}}\sigma_{Y},c_{Y}=\mu_{Y}\\
\end{align*}
where \mu_{X}, \mu_{Y},\sigma^2_{x},\sigma^2_{Y},\rho are constants\\
\\
\begin{itemize}
\item
Question 1):\\
Show that $(X,Y)$ has the bivariate normal pdf with parameter\\s $\mu_{X}, \mu_{Y},\sigma^2_{x},\sigma^2_{Y},\rho$\\
\item
Question 2):\\
if we start with bivariate normal parameters $$\mu_{X}, \mu_{Y},\sigma^2_{x},\sigma^2_{Y},\rho$, define constants $a_{x},b_{x},c_{x},a_{Y},b_{Y},c_{Y}$ as the solutions to the equations:\\
\begin{align*}
\mu_{X}=c_{X}, \sigma^2_{X}=a^2_{X}+b^2_{X},\\
\mu_{Y}=c_{Y}, \sigma^2_{Y}=a^2_{Y}+b^2_{Y},\\
\rho\sigma_{X}\sigma_{Y}=a_{X}a_{Y}+b_{X}b_{Y}
\end{align*}
  
\end{itemize}

\end{document}

A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 90​% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna​ sushi? 0.60  0.69  0.09  0.94  1.31  0.56  0.92

What is the confidence interval estimate of the population mean mu​?

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of  NFL teams for a season

a. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt (to 1 decimal). Enter negative value as negative number.

WIN%=______+_______*Yds/Att

b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

      WIN%=______+_______*INT/Att

c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

        WIN%=______+_______*Yds/Att+______*INT/Att

d. The average number of passing yards per attempt for the Kansas City Chiefs was 6.2 and the number of interceptions thrown per attempt was 0.036 . Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For a season the Kansas City Chiefs' record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

A toy manufacturer wants to know how many new toys children buy each year. A sample of 292 children was taken to study their purchasing habits. Construct the 80% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 5.6 Assume that the population standard deviation is 1.8. Round your answers to one decimal place.