(1 point) A random sample of 100100 observations from a population with standard deviation 13.8313.83 yielded a sample mean of 92.392.3.

1. Given that the null hypothesis is μ=90μ=90 and the alternative hypothesis is μ>90μ>90 using α=.05α=.05, find the following:
(a) Test statistic ==  
(b) P - value:  
(c) The conclusion for this test is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

2. Given that the null hypothesis is μ=90μ=90 and the alternative hypothesis is μ≠90μ≠90 using α=.05α=.05, find the following:
(a) Test statistic ==  
(b) P - value:  
(c) The conclusion for this test is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.

(a) What is P(X = 1 and Y = 1)?
P(X = 1 and Y = 1) = _____

(b) Compute P(X ≤ 1 and Y ≤ 1).
P(X ≤ 1 and Y ≤ 1) = ______

Compute the probability of this event.
P(X ≠ 0 and Y ≠ 0) =  

(d) Compute the marginal pmf of X.

Compute the marginal pmf of Y.

Using p_X(x), what is P(X ≤ 1)?
P(X ≤ 1) = ________

Suppose two people (let’s call them Julio and Karina) agree to meet for lunch at a certain restaurant, each person’s arrival time, in minutes after noon, follows a normal distribution with mean 30 and standard deviation 10. Assume that they arrive independently of each other and that they agree to wait for 15 minutes. If each person agrees to wait exactly fifteen minutes for the other before giving up and leaving.

h) Report the probability distribution of the difference (not absolute difference) in the arrival times of Julio and Karina. [Hint: You might let Tj represent Julio’s arrival time and Tk represent Karina’s arrival time, both in minutes after noon. Use what you know about normal distributions to specify the probability distribution of the difference D = Tj – Tk.]

i) Use appropriate normal probability calculations to determine the probability that the two people successfully meet. Also report the values of the appropriate z-scores. [Hint: First express the probability that they successfully meet in terms of the random variable D.]

j) Now let m represent the number of minutes that both people agree to wait, where m can be any real number. Determine the value of m so the probability of meeting is .9

k) Now suppose that Julio and Karina can only afford to wait for 15 minutes, but they want to have at least a 90% chance of successfully meeting. Continue to assume that their arrival times follow independent normal distributions with mean 30 and the same SD as each other. Determine how small that SD needs to be in order to meet their criteria. (As always, show your work.)

1 point) It is necessary for an automobile producer to estimate the number of miles per gallon achieved by its cars. Suppose that the sample mean for a random sample of 100100 cars is 28.228.2 miles and assume the standard deviation is 3.23.2 miles. Now suppose the car producer wants to test the hypothesis that μμ, the mean number of miles per gallon, is 29.829.8 against the alternative hypothesis that it is not 29.829.8. Conduct a test using α=.05α=.05 by giving the following:

(a)    positive critical zz score    

(b)    negative critical zz score    

(c)    test statistic    

The final conclustion is

A. We can reject the null hypothesis that μ=29.8μ=29.8 and accept that μ≠29.8μ≠29.8.
B. There is not sufficient evidence to reject the null hypothesis that μ=29.8μ=29.8.

The number of eggs that a female house fly lays during her lifetime is normally distributed with mean 840 and standard deviation 116. Random samples of size 82 are drawn from this population, and the mean of each sample is determined. What is the probability that the mean number of eggs laid would differ from 840 by less than 30? Round your answer to four decimal places.

If samples of size 39 are taken from a bimodal population, the distribution of sample means will be approximately normal. How can I be so sure of this?

A. The Law of Large Numbers says so
B. The Central Limit Theorem says so
C. The data is normal because the problem says so
D. It is a basic property of probability

You may need to use the appropriate appendix table to answer this question.

Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In 2018, the Amazon Alexa app was downloaded some 2,800 times per day from the Google Play store.† Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of 2,800 and standard deviation of 860.

(a)

What is the probability there are 2,100 or fewer downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(b)

What is the probability there are between 1,400 and 2,600 downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(c)

What is the probability there are more than 3,100 downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(d)

Suppose that Google has designed its servers so there is probability 0.02 that the number of Amazon Alexa app downloads in a day exceeds the servers' capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google's servers designed to handle? (Round your answer to the nearest integer.)

downloads per day

A survey found that​ women's heights are normally distributed with mean 62.6 in. and standard deviation 2.2 in. The survey also found that​ men's heights are normally distributed with a mean 67.3 in. and standard deviation 2.8. Complete parts a through c below. a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 8 in. and a maximum of 6 ft 2 in. Find the percentage of women meeting the height requirement. The percentage of women who meet the height requirement is ​%. ​(Round to two decimal places as​ needed.) b. Find the percentage of men meeting the height requirement. The percentage of men who meet the height requirement is ​%. ​(Round to two decimal places as​ needed.) c. If the height requirements are changed to exclude only the tallest​ 5% of men and the shortest​ 5% of​ women, what are the new height​ requirements? The new height requirements are at least in. and at most in. ​(Round to one decimal place as​ needed.)

Determine the margin of error for a 99​% confidence interval to estimate the population proportion with a sample proportion equal to 0.80 for the following sample sizes.

a. n=100             b. n=200             c. n=260

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.