Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.4 with sample standard deviation s = 3.0. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ > 7.4; H₁: μ = 7.4

H₀: μ = 7.4; H₁: μ > 7.4    

H₀: μ = 7.4; H₁: μ ≠ 7.4

H₀: μ = 7.4; H₁: μ < 7.4

H₀: μ ≠ 7.4; H₁: μ = 7.4

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since the sample size is large and σ is unknown.

The standard normal, since the sample size is large and σ is unknown.    

The Student's t, since the sample size is large and σ is known.

The standard normal, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.250

0.100 < P-value < 0.250    

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

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

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.

There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.    

Give a scientific method, procedure or ways to determine the statistics in order to investigate, or analyze the characteristic and behaviour of electric-powered two and three wheelers in terms of the factors such as safety, travel time, accessibility, cost for a user. I need help for a research class on determining the characteristic and behaviour of people.

) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following data are the rental vacancy rates in percentage (%) grouped by region for the first quarter of 2019 using a sample of 4 statistical metropolitan areas.

Vacancy rates (%)

Region Northeast South West
1 6 12 8

2 5 9 10

3 9 11 8

4 4 8 6

Sample Mean Sample   6 10 8

Variance 4.7 3.3 2.7

a.(10pt) Perform an ANOVA test to find if there are vacancy rates differences among the regions. Allow 1% error on your test.

b. (5pt) Do you think that the mean vacancy rate is the same for these regions? Why?

We consider 7 bags each containing 6 balls. Each ball is numbered from 1 to 6. The first 6 bags contain 6 balls where all numbers from 1 to 6 are present. The 7th bag contains 6 balls that all have the same number equal to 6. You take a bag randomly. You shoot a ball and put it back in its bag. You shoot another ball and you put it back in his bag and you observe that the two balls have the number 6. What is the probability of choosing the 7th bag?

On considère 7 sacs contenant chacun 6 balles. Chaque balle est numérotée de 1 à 6. Les 6 premiers sacs contiennent 6 balles où tous les numéros de 1 à 6 sont présents. Le 7-ième sac contient 6 balles qui ont toutes le même numéro égal à 6. Vous prenez un sac au hasard. Vous tirez une balle et vous la replacez dans son sac. Vous tirez une autre balle et vous la replacez dans son sac et vous observez que les deux balles ont le numéro 6. Quelle est la probabilité de choisir le 7-ième sac ?

Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. Assume σ ≈ 3.9 thousand dollars.

(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
thousand dollars per employee

(b) Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

(c) Let us say that you are the manager of a retail store with a large number of employees. Suppose the annual profits are less than 3 thousand dollars per employee. Do you think this might be low compared with other retail stores? Explain by referring to the confidence interval you computed in part (b).

Yes. This confidence interval suggests that the profits per employee are less than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.    

(d) Suppose the annual profits are more than 6.5 thousand dollars per employee. As store manager, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (b).

Yes. This confidence interval suggests that the profits per employee are greater than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.    

(e) Find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

Let us say that you are the manager of a retail store with a large number of employees. Suppose the annual profits are less than 3 thousand dollars per employee. Do you think this might be low compared with other retail stores? Explain by referring to the confidence interval you computed in part (b).

Yes. This confidence interval suggests that the profits per employee are less than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.    

Suppose the annual profits are more than 6.5 thousand dollars per employee. As store manager, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (b).

Yes. This confidence interval suggests that the profits per employee are greater than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.  

This is for Predictive Analytics.

1. Read the iris data set into a data frame.

2. Print the first few lines of the iris dataset.

3. Output all the entries with Sepal Length > 5.

4. Plot a box plot of Petal Length with a color of your choice.

5. Plot a histogram of Sepal Width.

6. Plot a scatter plot showing the relationship between Petal Length and Petal Width.

7. Find the mean of Sepal Length by species. Hint: You could use the tapply function. Other methods are also acceptable.

8. Use the subset function to extract only rows where the species is "versicolor."

9. Install the dplyr package and load it on your console.

10. Use a function in the dplyr package to show only rows with Sepal Length <6 belonging to species "virginica."

Submit all the code and subsequent output as a word file

Q1. An advertising company collected information from 10 Hollywood Movies, including the number of the first year box office reciepts ad the total promotional costs for each movies. They wish to study the relationship between promotion cost and the box office reciepts.

First year box office reciepts (millions) 85.1 106.3 50.2 130.6 54.8 30.3 79.4 91.0 135.4 89.3

Total promotional costs (millions) 5.10 5.80 2.10 8.40 2.90 1.20 3.70 7.60 7.70 4.50

a. If we would like to use the promotion cost to predict the box office reciepts, could you implement a simple regression model? Please use the matrix approach to estimate the reregression coefficients. Report your residual vector e, SSTO, SSR,SSE.

b. check the model assumption of residual assumptions. List all the assumptions made here and use graphs or tests to evaluate at least two of them. Report your R code/ output and your conclusions.

1. The service time in minutes from admit to discharge for ten patients seeking care in a hospital emergency department are 21, 136, 185, 156, 3, 16, 48, 28, 100, and 12.
   1. Use Minitab to construct a normal probability plot, an exponential probability plot, and a Weibull probability plot for these dat
   2. Do any of these distributions seem to be a reasonable probability model for the data? Explain your answer.

The number of incorrectly transferred calls made per month is listed below for a sample of 8 different months:
13 28 39 19 43 28 38 49
2.1 Calculate the mean number of incorrectly transferred calls made per month. Contextually interpret your answer. (3)
2.2 Calculate the median number of incorrectly transferred calls made per month. Contextually Interpret your answer. (3)

2.3 State the modal number of incorrectly transferred calls made per month. Contextually interpret your answer. (2)
2.4 Calculate the standard deviation for the number of incorrectly transferred calls made. (4)
2.5 Calculate Pearson’s median skewness coefficient for the number of incorrectly transferred calls made. Contextually interpret your answer. (3)
2.6 Which measure of central location would you use in your reporting – the mean, median or mode? Motivate your answer. (2)

A scientist has read that the mean birth weight μ of babies born at full term is 7.3 pounds. The scientist, believing that the mean birth weight of babies born at full term is less than this value, plans to perform a statistical test. She selects a random sample of 50 birth weights of babies born at full term. Suppose that the population of birth weights of babies born at full term has a standard deviation of 1.7 pounds and that the scientist performs her hypothesis test using the 0.01 level of significance.

Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

(If necessary, consult a list of formulas.)

Problem Details:

Sharona Medical Equipment, Ltd (fictional name) manufactures dental drills. The company has been experiencing problems with a specific part on the production line. Management suspects a machining problem has resulted in the length of a particular part varying outside of target specification limits. Management believes that the machine setting (1, 2, 3) and/or the shift (Morning, Afternoon, Night) during which the part is machined may explain the length errors. Management is particularly interested in the role the shift may play, as new hires are typically scheduled for night shifts. To investigate, four parts machined with each of the 3 settings were randomly selected from each of the 3 shifts. The deviation in length from the specified size was measured in microns and the collected data can be found in the “Machine_Shift_ProdErrors” worksheet in the Excel file titled Group Case #2 Data.

Requirements:

Your consulting firm has been hired to conduct a thorough analysis of the production error data and provide management of Sharona Medical Equipment, Ltd with a detailed summary of your analysis, conclusions reached, and any recommendations you feel qualified to make.

Data:

A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 14 of this year's entering students and finds that their mean IQ score is 116, with standard deviation of 14. The college records indicate that the mean IQ score for entering students from previous years is 111. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough evidence to conclude, at the 0.05 level of significance, that the mean IQ score, μ, of this year's class is greater than that of previous years?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

68 % of students at a school weight between 54 kg and 86 kg. Assuming this data is normally distributed, what are the mean and standard deviation?

Consider a possible linear relationship between two variables that you would like to explore

Define the relationship of interest and a data collection technique.

Determine the appropriate sample size and collect the data.

Perform the appropriate analysis to determine if there is a statistically significant linear relationship between the two variables.

Describe the relationship in terms of strength and direction.

Construct a model of the relationship and evaluate the validity of that model.