Suppose x has a distribution with μ = 22 and σ = 20. (a) If a random sample of size n = 37 is drawn, find μx, σ x and P(22 ≤ x ≤ 24). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(22 ≤ x ≤ 24) = (b) If a random sample of size n = 59 is drawn, find μx, σ x and P(22 ≤ x ≤ 24). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(22 ≤ x ≤ 24) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is part (a) because of the sample size. Therefore, the distribution about μx is .

this is the data for these set of questions . thank you very much please clearly represent The answer

1.)A plant species is being studied for the presence of cadmium and nickel levels near a former industrial waste site. Specifically, a researcher would like to know if distance to the industrial waste site is a predictor of Cadmium levels in the plant species. Perform the appropriate analysis using the Question 14 dataset in the Excel file. We can assume assumptions of test have been met. What is the slope of the equation from your analysis of the data? Use one of the following formats -9.999 or 9.999 depending on which is appropriate.

2.)You decide see how the addition of a second independent variable influences the results of the analysis from Question 14 (Cadmium vs. Distance and Angle). You add to the analysis the direction the plants were located in reference to the industrial waste site. The data is in the Angle column and represents the degrees off of magnetic north to where the plants were located. What is the p value from the analysis for Angle? Use the 0.999 format.

3.)For Question 14, the researcher would now like to know if there is a difference in mean Cadmium and Nickel concentrations in the plant species under investigation with both distance and angle from the industrial waste site. What kind of analysis should the research run?

4.)The researcher believes that there is a relationship between concentrations of Cadmium and Nickel. Run the appropriate analysis using the dataset for Question 14 in the Excel file and report on the r value.

Example 1
A pharmaceutical manufacturer does a chemical analysis to check the potency of products. The standard release potency for cephalothin crystals is 910. An assay of 16 lots gives the following potency data:

897 914 913 906 916 918 905 921 918 906 895 893 908 906 907 901

Assume the population standard deviation is 8 units. Test the hypothesis that the population mean potency is different from the standard release potency.

(1) Define the population quantity of interest in this study. This is called the population parameter.

(2) Carefully state the hypotheses to be tested about the population.
(3) What is the sample size?
(4) What quantity will be used as an estimate of the parameter from (1)? (5) What is the distribution of the sample estimate? Why?
(6) What is the standard deviation of the sample estimate?

(7) What is the value of the sample estimate for the sample in this study? (8) Find the test statistic. What does this measure?

(9) Give the p-value for the test in (2). What does this measure?

(10) Carefully state your conclusions.

(11) What assumptions have we made for this procedure to be valid?

If a random variable Xhas the gamma distributionwith α= 2and β = 1,

(a) What is the probability density functionf(x)?

(b) find P(1.8 < X< 2.4).

(c) What isE(X) and Var(X)?

(d) Put α= 1and β = 2.What isthe probability density functionf(x).

(e) What is the name of the distributionin (d)?

How many ways stated above may reduce Type II error?

Increasing sample size

Increasing alpha error

Increasing critical region size

Decreasing critical region size

A. 4

B. 1

C. 0

D. 3

E. 2

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

In a study of 794 randomly selected medical malpractice​ lawsuits, it was found that 517 of them were dropped or dismissed. Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.

In a study of cell phone usage and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 6993 subjects randomly selected from an online group involved with ears. There were 1343 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than​ 20%. Use the​ P-value method and use the normal distribution as an approximation to the binomial distribution.

Consider a drug testing company that provides a test for marijuana usage. Among 319 tested​ subjects, results from 27 subjects were wrong​ (either a false positive or a false​ negative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong.

Suppose you have a STAT class from 8:30–9:30 and an ECON class from 9:30–10:30. Assuming you arrive to school at 8:30 with zero text messages on your cell phone and you receive 6 texts every 45 minutes on average, find the following probabilities.

a)Based on the information above, find the probability that you receive at least 3 texts during your STAT class. N.B. I suggest you find these in R studio.

b)find the probability that you receive exactly 3 texts during your STAT and exactly 3 texts during ECON. I suggest you find these in R.

c)find the probability that you receive your 10th text during ECON.

Why is ANOVA more appropriate than multiple t-tests when comparing more than two groups?

A company claims that a new manufacturing process changes the mean amount of aluminum needed for cans and therefore changes the weight. Independent random samples of aluminum cans made by the old process and the new process are taken. The summary statistics are given below. Is there evidence at the 5% significance level (or 95% confidence level) to support the claim that the mean weight for all old cans is different than the mean weight for all new cans? Justify fully!

The Old process had a sample of size 25 with a mean of 0.504 and standard deviation of 0.019. The New process had a sample of size 25 with a mean of 0.495 and standard deviation of 0.021.

A company sells its product line in traditional brick and mortar stores as well an online store site. Historically, 42% of all company sales took place through its online store site. Due to recent budget cuts, the company has had to cut back on advertising expenditures that promote the online store site. You would like to determine if there has been a DECREASE in the proportion of sales coming from the online store site since the time you reduced your advertising expenditures. Therefore, the null and alternative hypotheses are:

                                H₀: proportion of online sales ≥ 42%         (no decrease in online sales proportion)

                                H₁: proportion of online sales < 42%         (decrease in online sales proportion)

You take a sample of 84 days and record what proportion of sales were online and what proportion were offline (in a traditional brick and mortar store). You utilize Minitab to create the analytics. The Minitab output is shown below.

Test and CI for One Proportion: ONLINE/OFFLINE

Method

Descriptive Statistics

Test

Find the p-value on the Minitab output. At a 95% confidence level, what is your conclusion regarding whether or not your company has experienced a decrease in the proportion of sales coming from the online store site. Justify your conclusion using the analytics.

What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 60 college students were surveyed and r = 11 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.24; H₁: p > 0.24H₀: p ≠ 0.24; H₁: p = 0.24    H₀: p = 0.24; H₁: p ≠ 0.24H₀: p = 0.24; H₁: p < 0.24

(b) What sampling distribution will you use?

The standard normal, since np > 5 and nq > 5.The Student's t, since np > 5 and nq > 5.    The Student's t, since np < 5 and nq < 5.The standard normal, since np < 5 and nq < 5.

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


(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)


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

A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to receive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. The data are recorded as follows.

Is there a difference in change in symptoms by treatment group? Run the appropriate test at a 5% level of significance.

Consider observations of the number of wins per season by National Football League teams over the years 1989-2008. The observed mean is 8 wins/season and the observed standard deviation is 3.02. A histogram illustrates these data.

Referring to these NFL data and assuming normality, the probability that a randomly chosen team wins 11 or more games is?

Group of answer choices

a. 0.16

b. 0.25

c. None of these options

d. 0.09

e. 0.37