Industrial wastes and sewage dumped into our rivers and streams absorb oxygen and thereby reduce the amount of dissolved oxygen available for fish and other forms of aquatic life. One state agency requires a minimum of 5 parts per million (ppm) of dissolved oxygen in order for the oxygen content to be sufficient to support aquatic life. Six water specimens taken from a river at a specific location during the low-water season (July) gave readings of 4.9, 5.0, 5.0, 5.0, 5.0, and 4.6 ppm of dissolved oxygen. Do the data provide sufficient evidence to indicate that the dissolved oxygen content is less than 5 ppm? Test using α = 0.05.

H₀: μ = 5 versus H_a: μ < 5    

State the test statistic. (Round your answer to three decimal places.)

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

The university claims that the average cost of accommodation(μo) within five kilometers is 2000 JD per academic year. A university student is preparing her budget for her first year at the university. She is concerned that the university’s estimate is too low. Having taken AP statistics, she decides to perform the following test of Hypothesis; Ho: μ = 2000 JD Ha: μ ˃ 2000 JD (a)- Describe the type I and type II for this problem (b)- Which of the two errors I or II has more serious consequences for the student, and Why?

Subject: Probability and statistics

Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of μ = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 37 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 16.4 ft; H1: μ ≠ 16.4 ft H0: μ < 16.4 ft; H1: μ = 16.4 ft H0: μ > 16.4 ft; H1: μ = 16.4 ft H0: μ = 16.4 ft; H1: μ < 16.4 ft H0: μ = 16.4 ft; H1: μ > 16.4 ft (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 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 unknown. 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 two 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. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (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 = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 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 0.01 level to conclude that the storm is increasing above the severe rating. There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

The line graph shown below represents the number of TVs in a house by the square footage (in hundreds of feet). According to the information

. A researcher selects a random sample of 10 persons from a population of truck drivers and gives them a driver’s aptitude test. Their scores are 22,3,14,8,11,5,18,13,12, and 12.

     (a) Find the estimated standard error of the mean.

     (b) Find the 95% confidence interval for the population mean.

The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $8040. Assume that the standard deviation is $4800. The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law.

What is the probability that the sample mean tax is less than $1800?

What is the probability that the sample mean tax between $7400 and $8000?

40th percentile of the sample mean is ?

Give a real-life data example for each of the following three cases:

(a) False negatives are less tolerable than false positives.

(b) False positives are less tolerable than false negatives.

(c) False positives and false negatives are of equivalent importance.

In a study of cellphone use and brain hemispheric dominance, an Internet survey was e-mailed to 5000 subjects randomly selected from an online group involved with ears. 717 surveys were returned. Use a 0.01 significance level to test the claim that the return rate is less than 15%.

QUESTION 1

Studd Enterprises sells big-screen televisions. A concern of management is the number of televisions sold each day. A recent study revealed the number of days that a given number of televisions were sold.

                        # of TV units sold      # of days

                                       0                             2

1.                         4

2.                       10

3.                       12

4.                         8

5.                         4

Answer the questions below. For each part, show your calculations and/or explain briefly how you arrived at your answer, as appropriate or needed.

Required:

1. Convert the frequency distribution above into a probability distribution (or relative frequency distribution) showing the proportion of days (rather than the number of days) that the number of televisions sold was 0, 1, 2, 3, 4, and 5 respectively. ( 3 marks)

2. Compute the mean of this general discrete probability distribution. ( 3 marks)

3. Compute the standard deviation of this general discrete probability distribution. ( 5 marks)

4. What is the probability that exactly 4 televisions will be sold on any given day? ( 1 mark)

5. What is the probability that 2 or more televisions will be sold on any given day? ( 1 mark)

6. What is the probability that less than 2 televisions will be sold on any given day? (1 mark)

g What is the probability that between 1 and 4 televisions inclusive will be sold on any given day? (1 mark)

Based upon extensive data from a national high school educational testing​ program, the mean score of national test scores for mathematics was found to be 605 and the standard deviation of national test scores for mathematics was found to be 98 points. What is the probability that a random sample of 196 students will have a mean score of more than 610? Less than 591​?

a) The probability that a random sample of 196 students will have a mean score of more than 610 is ?

b) The probability that a random sample of 196 students will have a mean score of less than 591 is ?

In a certain high school, uniforms are optional. A study shows that high school students who wear uniforms have a lower grade average than students who don't wear uniforms. From this study, the school administration claims that they should not require the students to wear uniforms because that is the cause of the lowering grades. Another possible explanation is that students who wear uniforms are poorer than the students who don't wear uniforms and the economic situation of their parents is causing the lower grades.

a) What is the explanatory variable in this study?
economic situation
poorer grades.
wearing a uniform.

b) What is the response variable in this study?
economic situation
wearing a uniform.
poorer grades.

c) What is the lurking variable in this study?
poorer grades.
wearing a uniform.
economic situation

d) Draw a diagram that explains your answers. (Possible diagrams are causation, common response, or confounding). Be sure to label all variables in the diagram

The following data gives the number of hours 7 students spent studying and their corresponding grades on their midterm exams. Hours Spent Studying 1 1.5 3 3.5 4 4.5 5.5 Midterm Grades 60 63 75 78 84 87 93 Step 2 of 3 : Determine if r is statistically significant at the 0.01 level.

Please indicate which type of sampling design is most appropriate for each of the following studies. The choices are SRS, stratified random sampling, and matched pair design.

(1).A researcher wants to know the effect of climate change on the percent yield of the corn harvest. They collected the data for the same 50 plots in both 2016 and 2017 for their study.

(2).A developer in West Lafayette wants to know if students who are renting off-campus like their apartment complex. They chose 10 students who lived in 5 different complexes.

(3).A pharmaceutical company wants to determine if the size of a new pill is too large to take. They randomly select 200 people and asked if they could swallow the pill or not.

(4).A rice manufacturer chose 100 single servings to test to be sure that there is no more 10 ppb of arsenic in them to assure to their customers that the product is safe to eat.

(1 point) The amount of paper used in a year per person in America has a normal (bell-shaped)distribution with a mean of 650 pounds and a standard deviation of 150pounds.

a)What percent of Americans use between200 and 1100 pounds of paper per year?

b)What percent of Americans use more than 800 pounds of paper per year?

c)What percent of Americans use more than 350 pounds of paper per year?

Here are some prices for randomly selected grocery items from the grocery store:

Items Prices:

Cheese $3.29

Butter $4.99

Eggs $3.49

Yogurt $3.49

Juice $3.89

Tea $3.69

Chips $3.99

Soda $1.99

Pastry $2.99

Cerrial $4.99

Oats $3.29

Almond Milk $2.79

Almonds $4.39

Popcorn $3.29

Crackers $3.59

Ice Cream $6.99

Cookies $2.99

Jam $3.69

Peanut Butter $3.29

Coffee $3.19

Green Tea $4.99

BBQ Sauce $2.99

Oil $6.69

Mayonnaise $4.59

Mustard $2.99

1. Compute the sample mean x and the sample standard deviation of grocery store prices.

2. State the population mean µx and population standard deviation σx of sample mean in terms of population mean and population standard deviation for the original variable x.

3. Construct the 95% confidence interval for the mean grocery prices. Standard deviation $1.10  

4. Compute the minimum sample size required to have margin of error at most $ 0.30, while keeping the confidence level at 95%. Standard Deviation is $1.10

5. Construct the 95% confidence interval for the mean grocery store prices. (This time assume that the standard deviation σx is unknown).

6. Suppose the mean grocery price for Safeway is known to be $ 4.10. Test the hypothesis that the mean grocery price for this grocery store vs from mean another grocery stores price with significance level α = 0.10. Standard deviation is $1.10

7. Retest the hypothesis that the mean grocery price for this grocery store vs mean another grocery stores price at significance level α = 0.10. (This time, assume that the standard deviation σx is unknown).

This is for the purposes of checking answers and comparing work. Thank you.