The following data show weight (in kg) of 24 women in a study: 46.4, 53.2, 52.8, 42.0, 50.8, 43.0, 51.9, 59.2, 55.1, 38.9, 49.7, 49.9, 43.1,42.2, 52.7, 49.8, 50.7, 44.8, 49.2, 47.7, 42.9, 52.9, 54.1, 45.4. Prepare the following:

I. A frequency distribution,

II. A relative frequency distribution,

III. A cumulative frequency distribution,

IV. A cumulative relative frequency distribution,

V. A stem-and-leaf plot, and

VI. Comment on the findings.

Using Rcode solve

A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and sample standard deviation is 4.83 mpg.

a. Which kind of confidence interval is appropriate to use here, z-interval or t-interval?

b. What are the assumptions to check for the interval you chose?

c. Please use R to find the critical value the company needs when constructing a (two-sided) 98% CI.

d. Please use R to construct a (two-sided) 98% CI for the mean of the general gasoline usage.

e. Please use R to construct a 98% upper confidence bound for the mean of the general gasoline usage.

f. Create a R function whose argument is the width of CI, and the output is the sample size necessary to achieve such accuracy. The confidence level is fixed at 98%.

g. Apply the function you created in part (f) to demonstrate that larger sample size is required to achieve better accuracy (i.e, narrower CI width). Confidence level is fixed at 98%. Show at least three examples

A furniture store has maintained monthly sales records for the past 20​ months, with the results shown below.

Assume you have determined there is NO SEASONALITY in this time series.​ Therefore, you want to fit a linear trend model​ (that is, trend​ only) to the data.

Calculate the linear trend equation.​ (Round coefficients to the nearest whole​ number.)

y Subscript t Baseline equalsyt=nothing​+

nothing​*t

What are the test statistic and​ p-value to test for a significant trend. Round both to two decimal places.

T​ = nothing

​p-value = nothing

Is the trend significant using a​ 10% significance​ level?

Yes

No

What is the value of​ R-squared? (Round to two​ decimals.)

nothing

Forecast the sales for the next month​ (t =​ 21). (Round to the nearest whole​ number.)

Upper F 21 equalsF21=nothing

Based on the​ R-squared value, how confident are you in this​ forecast? (That​ is, how accurate do you think the forecasts will​ be?)

A.

Not confident at all because the​ R-squared value is so low

B.

Very confident because the​ R-squared value is high

C.

Somewhat confident because the​ R-squared value is moderate​ (not extremely high but not extemely​ low)

An evolutionary psychologist hypothesizes that people will increase from the standard 24-hour sleeping and walking cycle if not exposed to the usual pattern of sunlight. To test this notion, a sample of volunteers were placed (individually) in a room in which there was no outside sunlight, no clocks, and other indications of time. They stayed in the room for a month and could turn the lights on and off as they pleased. What can the psychologist conclude with α = 0.01? The data are below.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- the volunteers 24-hour cycle no outside sunlight lights on lights off
Sample:
---Select--- the volunteers 24-hour cycle no outside sunlight lights on lights off

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

People significantly increase from the 24-hour sleeping and walking cycle if not exposed to the usual pattern of sunlight.

People significantly decrease from the 24-hour sleeping and walking cycle if not exposed to the usual pattern of sunlight.    

People do not significantly change from the 24-hour sleeping and walking cycle if not exposed to the usual pattern of sunlight.

In a clinical study of an allergy drug, 109 of the 202 subjects reported experiencing significant relief from their symptoms. at the .01 significance level, test the claim that more than 50% of those using the drug experienced relief. what is the final conclusion in simple nontechnical terms?

Provide the goal of the study, clearly stating the research hypothesis. Describe the study design.

Describe the results noting the direction (e.g., higher or lower; increase or decrease; etc.) and difference between sample mean (M = ?; 95% CI = ?) and the population mean (µ = ?).

Report the inferential statistic used to compute the p-value (Z [ n = ?] = observed value, p < or > .05) and state if the results are significant or not.

Report and interpret the 95% CI around the difference between the two means (e.g., does the CI contain 0 or not—how do you interpret the Ho if it does or does not include 0?). Also, be sure to report and interpret the effect size (d = ?).

1. A research team happens to know that male rats administered a placebo drug will spend μ = 5 minutes per hour grooming (σ = 6). They believe that male rats administered a low dose of the street drug ecstasy will spend less than 5 minutes per hour grooming. They chose 100 male rats, administered a low dose of ecstasy to each, then measured the number of minutes per hour each rat spent grooming. The mean of this sample was M = 4. The research question the researcher want to answer is: does administering a low dose of ecstasy affect the time spent grooming?

1. Chris and Pat both work independently on the same computer program. The probability Chris’ program works is 10% and the probability Pat’s program works is 15%. What is the probability exactly one of their programs works?  

2. Terry and pat both play independently with the same computer game. The probability Terry will score a victory is 30% and the probaabiltythat Pat wwill score a victory is 25%. What is the probability that at least one of them scores a victory?

Can someone provide me the formula, or statement, to calculating the P-value given a (1) z-statistic value, (2) t-statistic value, and (3) f-statistic value (include left tail, right tail, two-tailed for all 3). I've searched all over but the descriptions and videos just don't cut it. They just look at the respective table and pop a value out of no where without providing an actual formula or statement that says given this statistic, use this formula, or follow these simple steps. It's always here is the table, and seconds later, out comes a P-value without writing anything down, showing their work.

Is there any difference among population means? Please show steps to completion.

How do you compute SS, MS, and F values by hand?

Including critical and computed values show steps of how to obtain.

alpha = 0.05
set 1
27
23
17
21
xbar= 22
s = 4.16

set 2
21
28
25
18
xbar = 23
s= 4.40

set 3
33
28
23
20
xbar = 26
s = 5.71

How Laude? Many educational institutions award three levels of Latin honors often based on GPA. These are laude (with high praise), magna laude (with great praise), and summa laude (with highest praise). Requirements vary from school to school. Suppose the GPAs at State College are normally distributed with a mean of 2.95 and standard deviation of 0.43.

(a) Suppose State College awards the top 2% of students (based on GPA) with the summa laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.
? GPA or higher

(b) Suppose State College awards the top 10% of students (based on GPA) with the magna laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.
?? GPA or higher

(c) Suppose State College awards the top 20% of students (based on GPA) with the laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.
?? GPA or higher

Can someone please describe the relationship between p-value and alpha value (0.05) in the ANOVA and provide a good example

regular gasoline averaged $2.75 per gallon in the United States in March 2010. Assume the standard deviation for gasoline prices is $0.08 per gallon. A random sample of 30 service stations was selected.

a) What is the probability that the sample mean will be less than $2.77?

b) What is the probability that the sample mean will be more than $2.76?

c) What is the probability that the sample mean will be between $2.72 and $2.78?

d) Suppose the sample mean is $2.79. Does this result support the findings of AAA? Explain your answer.

The lengths of a particular animal's pregnancies are approximately normally distributed, with mean μ equals=271

days and standard deviation σ equals=20days.

(a) What proportion of pregnancies lasts more than 286 days?

(Round to four decimal places as needed.)

(b) What proportion of pregnancies lasts between 256 and 281 days?

(Round to four decimal places as needed.)

(c) What is the probability that a randomly selected pregnancy lasts no more than 266 days?

(Round to four decimal places as needed.)

(d) A "very preterm" baby is one whose gestation period is less than 226 days. Are very preterm babies unusual?

(Round to four decimal places as needed.)

The probability of this event is _____ so it _____ be unusual because the probability is _______ than 0.05.

(Round to four decimal places as needed.)

Jobs arrive at the server is a Poisson random variable with a mean of 360 jobs per hour. Find:

1. The probability of at least 8 jobs arriving in the interval [8:00, 8:02] a.m.
2. The probability of at most 8 jobs arriving in the interval [9:15, 9:18] p.m.
3. Using the exponential distribution (and its relation to the Poisson) find the probability of no jobs arriving in the interval [7:00, 7:01] p.m.

A study is run in which 900 individuals are sampled and each is classified as to whether they had contracted the flu during the last year and whether they had been inoculated for the flu. The research question is whether inoculation status and contracting the flu are associated and what is the magnitude of the association.

Do a chi-square test to see if there is an association between inoculation and getting the flu.

1. What would be the null and alternate hypothesis for this question?

2. if the p-value is 0.006, Statement of conclusion both as “reject or fail to reject the null hypothesis” and as a verbal statement explaining the meaning of that conclusion in this context.