A soil scientist has just developed a new type of fertilizer and she wants to determine whether it helps carrots grow larger. She sets up several pots of soil and plants one carrot seed in each pot. Fertilizer is added to half the pots. All the pots are placed in a temperature-controlled greenhouse where they receive adequate light and equal amounts of water. After two months of growth, the scientist harvests the carrots and weighs them (in kilograms). Below is a data table showing the weight of the carrots at the end of the growing period from the two treatment groups. Here is a hyperlink to the data.

When analyzing this dataset with a t-test, the  hypothesis states that the average size of the carrots from each treatment are the same, whereas the  hypothesis states that the fertilized carrots are larger in size.

To analyze this data set, the scientist should use a -tailed t-test.

After performing a t-test assuming equal variances using the data analysis add-in for MS Excel, what is the calculated t-value for this data set?

Round your answer to four decimal places.

Your answer should be a positive value.

Report the appropriate critical t value, based on your decision of a one- or two-tailed test, calculated by MS Excel using the Data Analysis add-in.

Round your answer to four decimal places.

What is the appropriate p value for the t-test?

Report your answer in exponential notation

Report your answer to 4 decimal places after converting to exponential notation

e.g.

1.1234E-01 for 0.112341

3.1234E-04 for 0.000312341

Would you reject or fail to reject the null hypothesis?

A telemarketing firm is monitoring the performance of its employees based on the number of sales per hour. One employee had the following sales for the last 19 hours

9,5,2,6,5,6,4,4,4,7,4,4,7,8,4,4,5,5,4

What is the mode, median and mean for the distribution of number of sales per hour?

What is the first and third quartile for the distribution of number of sales per hour?

For the distribution of sales per hour, what is the interquartile range?

Draw a dot plot for the data

A researcher hypothesizes that reaction time (RT) measured in milliseconds in response to a startling stimulus will be lower (faster) before people drink 5 beers than it will be afterward. A sample of 12 patients is presented with a startling stimulus, and their mean score is 6.08 milliseconds with an SD of 1.38. They drink 5 beers, another startling stimulus is presented, and participants’ mean reaction time is 14.25 milliseconds with an SD of 3.7. The raw scores and Z-scores were as follows:

RT before: 7 8 7 8 5 6 6 5 3 6 6 6

Z before: 0.97,1.79,0.97,1.79,-0.69, 0.14, 0.14, -0.69, -2.34, 0.14,0.14,0.14

RT after: 16,19,15,15,14,15,13,12,4,15,16,17

Z after: 0.49,1.34,0.21,0.21,-0.07,0.21,-0.35,-0.64,-2.90,0.21,0.49,0.78

Test the researcher’s hypothesis at α = .05.

state which statistical test you should use, (e.g., single-sample t- test, paired-samples t- test etc.) Show the value of the obtained inferential statistic (e.g.,t= 2.17), the degrees of freedom

and the critical value from the relevant table, and state whether you should reject or accept the null hypothesis ,Calculate effect size when applicable.Then explain, in non-statistical language

(completely in layperson’s terms) what the practical conclusion of your analysis is, including the direction of the effect.

The file SAT Excel data lists the average high school student scores on the SAT exam by state. There are three components of the SAT: Critical reading, math and writing. These components are listed in Excel. Also, the sum of all 3 components (The Combined column) is listed. The percentage of all potential students who took the SAT is listed by state. Use Excel to help you answer the following questions. Find the mean, median, and mode for each of the numerical variables. For each of the numerical variables, which is the most appropriate measure of central tendency and explain why.

In a test of the effectiveness of garlic for lowering​ cholesterol, 45 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes ​(beforeminus​after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 3.2 and a standard deviation of 17.3. Construct a 90​% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol?

Instructions This assignment is to be typed up in the supplied R-Script. You need to show all of your work in R in the given script. Be sure and use # in front of any text that you type in. You are allowed to work with your peer group, but please site your sources! If you get help from anyone, you need to mention that in your write up. This assignment is worth 60 points (10 per problem) and you can use it to replace the online Midterm Quiz. That is, if you chose to, you can count it twice.

6. Minimum wage. A Rasmussen Reports survey of 1,000 US adults found that 42% believe raising the minimum wage will help the economy. Construct a 99% confidence interval for the true proportion of US adults who believe this.

2.. The SVPA sells a box of 6 Blue Hubbard pumpkins. The mean weight of all the pumpkins in the box is 14.5 lbs. The table below shows the distribution of the sample mean weight if 3 pumpkins are selected randomly from the box.

a. Suppose the three pumpkins selected are 3lbs, 9 lbs and 21 lbs. Construct a 60% confidence interval on the population mean using this sample. Explain how you figured out the margin of error.

b. Interpret the 60% confidence interval found in part a. Give the full interpretation and use the context of the problem

c. The SVPA claims that based on years of data the mean weight of the pumpkins in the box is 14.5 lbs. Does the 60% confidence interval from part a contradict this claim?

d. What is the probability the mean weight of the pumpkins in the box is in the 60% confidence interval found in part a. Explain.

e. For the hypotheses H₀: μ = 14.5 lbs and H₁: μ ≠ 14.5 lbs on the mean weight of the pumpkins in the box, what would the p-value be for the hypothesis test using the sample from part a. Use correct notation. Explain what the p-value represents within the context of the problem.

f. For the hypothesis test in part e, what would be the lowest significance level at which we would reject the null hypothesis? Explain.

Construct a confidence interval of the population proportion at the given level of confidence. x equals 175 comma n equals 250 comma 90 % confidence

The lower bound is _____.

The upper bound is _____. ​(Round to three decimal places as​ needed.)

Measurements of length (cm) were taken for a sample of fish. The gender (male or female) of each fish was also recorded.

The most appropriate technique to explore whether there is a difference in the mean weights of fish between males and females would be:

Select one:

a. 1 sample z-test

b. testing for two proportions

c. 2 sample t-test.

d. 1 sample t-test

Consider the following claim: “ The majority of U.S. residents are right-handed” Which one of these is correct?

Question:-6 people were randomly selected and their systolic (x) and diastolic (y) blood pressures were measured. Systolic 138 130 135 140 120 125 Diastolic 92 91 100 100 80 90 Σx = 788, Σy = 553, Σx 2 = 103794, Σy 2 = 51245, Σxy = 72876 (Data)

(A)If systolic blood pressure increases by one unit, then:-

(a) diastolic blood pressure decreases by about 15.5 units

b) diastolic blood pressure decreases by about 0.82 units.

(c) diastolic blood pressure increases by about 15.5 units

(d) diastolic blood pressure increases by about 0.82 units

(e) the response of the diastolic blood pressure cannot be predicted (Explain in detail how..??)

(1 point) a) For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.46 million dollars. Assuming a population standard deviation gross earnings of 0.52 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions).
Confidence interval: ( , ).

b) Which of the following is the correct interpretation for your answer in part (a)?
A. There is a 99% chance that the mean gross earnings of all Rolling Stones concerts lies in the interval
B. We can be 99% confident that the mean gross earnings of all Rolling Stones concerts lies in the interval
C. We can be 99% confident that the mean gross earnings for this sample of 30 Rolling Stones concerts lies in the interval
D. None of the above

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

Salary   Education
40   4
73   1
99   7
57   1
83   8
76   4
109   6
49   0
31   4
32   4
91   2
40   4
65   6
71   2
166   5
61   0
88   1
59   4
132   9
25   0

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 2 decimal places.)

Salaryˆ=

+ Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,220.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,220.

c. What is the predicted salary for an individual who completed 5 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

Salaryˆ               $

Instructions This assignment is to be typed up in the supplied R-Script. You need to show all of your work in R in the given script. Be sure and use # in front of any text that you type in. You are allowed to work with your peer group, but please site your sources! If you get help from anyone, you need to mention that in your write up. This assignment is worth 60 points (10 per problem) and you can use it to replace the online Midterm Quiz. That is, if you chose to, you can count it twice. 1. Data type and plots. We collected in the MTTH class a set of paired data on age and gender. The data set is given in the supplied R-Script and is repeated here: age = c(25, 20, 21, 21, 18, 18, 18, 18, 18, 18, 21, 21, 18, 18, 19 ,17 ,18, 18, 20, 18, 19, 17, 22, 19, 18, 18, 20, 17, 18, 18, 25) gend = c(”f”, ”m”, ”m”, ”m”, ”m”, ”f”, ”m”, ”f”, ”f”, ”m”, ”m”, ”f”, ”f”, ”f”, ”m”, ”m”, ”f”, ”m”, ”f”, ”f”, ”f”, ”m”, ”m”, ”m”, ”f”, ”m”, ”f”, ”f”, ”f”, ”m”, ”f”) (USING RSTUDIO)

(a) What type of variable is ”age”?

(b) What type of variable is ”gend”?

(c) What are the mean, median, standard deviation, and IQR for the ”age” data?

(d) Give a boxplot and histogram for the ”age” data. What is the shape of the distribution?

(e) Give a barplot for the ”gend” variable. Does is make sense to ask what the shape of this plot is? Why?

(f) Give a 98% confidence interval for the population proportion of females enrolled in Math 15 at College of the Redwoods.

A baseball fan wanted to know if there is a difference between the number of games played in a World Series when the American League won the series versus when the national league won the series. From 1922 to 2012 the population standard deviation of games won by the American League was 1.14, and the population standard deviation of games won by the National League was 1.11 of 19 randomly selected World Series of games won by the American League, the mean number of games won was 5.76. the mean number of 17 randomly selected games won by the national League was 5.42.

a) State and label the two population or samples.

b) What is function that you used on the calculator(TI-84) and what are the inputs?

c) Use the Five Method to do the Hypothesis Test.