The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 21 points on this test, rounded to five decimal places?

(b) What is the 63 percentile of the distribution of test scores, rounded to three decimal places?

Warranty: You buy a cell phone for $90 and there is a 6% chance that it will fail. You can pay an additional $3 for the hassle-free replacement warranty. This means if it fails you will get a free replacement.

(a) Suppose you do not buy the warranty but will buy a second one if the first one fails (we will assume this second one does not fail) and you will pay the full $90 for the second one. Complete the following table to assist in calculating the expected cost for this phone. Enter the probabilities to 2 decimal places.

(b) Use the table to calculate the expected value for the cost of this phone. Round your answer to the nearest penny.
$

(c) Considering the expected cost above and the price of the warranty ($3), did you make the right decision to not buy the warranty and why? There is only one correct answer and explanation.

Yes, because the expected cost is less than the cost of the phone plus the warranty.No, because the expected cost is greater than the cost of the phone plus the warranty.    Yes, because the expected cost is greater than the cost of the phone plus the warranty.No, because the expected cost is less than the cost of the phone plus the warranty.

The variable x is normally distributed with a mean of 500 and a standard deviation of 50. Find a) The 60th percentile. b)The 35th percentile. c)The x value which exceeds 80% of all x values. d)The x value that is exceeded by 80% of all x values.

An important quality characteristic used by the manufacturers of ABC asphalt shingles is the amount of moisture the shingles contain when they are packaged. Customers may feel that they have purchased a product lacking in quality if they find moisture and wet shingles inside the packaging. In some cases, excessive moisture can cause the granules attached to the shingles for texture and colouring purposes to fall off the shingles resulting in appearance problems. To monitor the amount of moisture present, the company conducts moisture tests. A shingle is weighed and then dried. The shingle is then reweighed, and based on the amount of moisture taken out of the product, the pounds of moisture per 100 square feet is calculated. The company would like to show that the mean moisture content is less than 0.35 pound per 100 square feet. The file (A & B shingles.csv) includes 36 measurements (in pounds per 100 square feet) for A shingles and 31 for B shingles. 3.1. For the A shingles, form the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feet. 3.2. For the A shingles, conduct the test of hypothesis and find the p-value. Interpret the p-value. Is there evidence at the 0.05 level of significance that the population mean moisture content is less than 0.35 pound per 100 square feet? 3.3. For the B shingles, form the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feet. 3.4. For the B shingles, conduct the test of the hypothesis and find the p-value. Interpret the p-value. Is there evidence at the 0.05 level of significance that the population mean moisture content is less than 0.35 pound per 100 square feet? 3.5. Do you think that the population means for shingles A and B are equal? Form the hypothesis and conduct the test of the hypothesis. What assumption do you need to check before the test for equality of means is performed? 3.6. What assumption about the population distribution is needed in order to conduct the hypothesis tests above? 3.7. Check the assumptions made with histograms, boxplots, normal probability plots or empirical rule. 3.8. Do you think that the assumption needed in order to conduct the hypothesis tests above is valid? Explain.and please send me python commands

SHOW STEPS IN EXCEL PLEASE

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

(a)

The estimated regression equation for this data is

ŷ = 22.726 + 0.323x,

where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₀ = 0
H_a: β₀ ≠ 0    H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ ≥ 0
H_a: β₁ < 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We conclude that the relationship between price ($) and overall score is significant.     Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b)

Test for a significant relationship using the F test. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₀ ≠ 0
H_a: β₀ = 0    H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We conclude that the relationship between price ($) and overall score is significant.     Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(c)

Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

If n=13, ¯(x-bar)=47, and s=2, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place

T-Test Problems (show your work)

A researcher wishes to determine if a particular drug affects pilot reaction time to air traffic controller instructions. The researcher has 10 pilots. The pilots are observed in normal performance and their reaction times are recorded. Then the pilots are administered the drug, observed again, and their reaction times are recorded. The expectation is that the drug will reduce reaction time.

Conduct a t test using the five-step hypothesis testing process

A wholesale distributor operating in different regions of Portugal has information on annual spending of several items in their stores across different regions and channels. The data (Wholesale Customer.csv) consists of 440 large retailers’ annual spending on 6 different varieties of products in 3 different regions (Lisbon, Oporto, Other) and across different sales channel (Hotel/Restaurant/Café HoReCa, Retail).

1.1. Use methods of descriptive statistics to summarize data.
Which Region and which Channel seems to spend more?
Which Region and which Channel seems to spend less?

1.2. There are 6 different varieties of items are considered.
Do all varieties show similar behaviour across Region and Channel?

1.3. On the basis of the descriptive measure of variability, which item shows the most inconsistent behaviour?
Which items shows the least inconsistent behaviour?

1.4. Are there any outliers in the data?

1.5. On the basis of this report, what are the recommendations?

How do I attach file, unable to paste data..also send me python commands for this answer

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 34 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 22 feet. (You may find it useful to reference the appropriate table: z table or t table) b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

In a​ study, researchers wanted to measure the effect of alcohol on the hippocampal​ region, the portion of the brain responsible for​ long-term memory​ storage, in adolescents. The researchers randomly selected

1818

adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of

9.029.02

cm cubedcm3.

An analysis of the sample data revealed that the hippocampal volume is approximately normal with

x overbarxequals=8.078.07

cm cubedcm3

and

sequals=0.80.8

cm cubedcm3.

Conduct the appropriate test at the

alphaαequals=0.010.01

level of significance.

State the null and alternative hypotheses.

Upper H 0H0​:

muμ

▼

less than<

not equals≠

greater than>

equals=

nothing

Upper H 1H1​:

muμ

▼

equals=

less than<

greater than>

not equals≠

nothing

​(Type integers or decimals. Do not​ round.)

Identify the​ t-statistic.

t 0t0equals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

Make a conclusion regarding the hypothesis.

▼

Reject

Fail to reject

the null hypothesis. There

▼

is

is not

sufficient evidence to claim that the mean hippocampal volume is

▼

greater than

less than

equal to

nothing

cm cubedcm3.

Scientists are interested in human recall and memory. Is it easier to memorize words that have "meaning"? To study this problem, two lists of 20 three-letter "words" were used. One list contained meaningful words (e.g., CAT, DOG), whereas the other list contained nonsense words (e.g., ATC, ODG). A ninth grade class of thirty students will be divided into two groups of students. One group was asked to memorize the list of meaningful words; the other group was asked to memorize the list of nonsense words. The number of words correctly recalled by each student was tabulated.

Number of meaningful words recalled: 12,15,12,12,10,3,7,11,9,14,9,10,9,5,13

Number of nonsense words recalled: 4,6,6,5,7,5,4,7,9,10,8,7,3,2

Is there convincing evidence to report that meaningful words are remembered better than nonsene words?

What statistic test would you use to prove that?

It is estimated that 0.5% of the callers to the billing department of a local telephone company will receive a busy signal.

What is the probability that of today's 1350 callers at least 5 received a busy signal? Use the poisson approximation to the binomial. (Round the final answer to 4 decimal places.)

Probability             

Steele Electronics Inc. sells expensive brands of stereo equipment in several shopping malls. The marketing research department of Steele reports that 35% of the customers entering the store that indicate they are browsing will, in the end, make a purchase. Let the last 20 customers who enter the store be a sample.

a. How many of these customers would you expect to make a purchase? (Round the final answer to the nearest whole number.)

Number of Customers            

b. What is the probability that exactly six of these customers make a purchase? (Round the final answer to 4 decimal places.)

Probability            

c. What is the probability 11 or more make a purchase? (Round the final answer to 4 decimal places.)

Probability            

d. Does it seem likely at least one will make a purchase ("likely" refers if the probability is more than 70%)?

(Click to select)  Yes  No

1. Complaints about an Internet brokerage firm occur at a rate of 3 per day. The number of complaints appears to be Poisson distributed.

A. Find the probability that the firm receives 3 or more complaints in a 2-day period.

2. In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 13% of voters are Independent. A survey asked 15 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that more than 3 people are Independent?

The parking authority in downtown Halifax reported the following information for a sample of 260 customers on the number of hours cars are parked and the amount they are charged:

a-1. Convert the information on the number of hours parked to a probability distribution. (Round the final answers to 3 decimal places.)

a-2. Is this a discrete or a continuous probability distribution?

(Click to select)  Discrete  Continuous

b-1. Find the mean and the standard deviation of the number of hours parked. (Round the final answers to 3 decimal places.)

Mean            

Standard deviation            

b-2. How would you answer the question, how long is a typical customer parked? (Round the final answer to 3 decimal places.)

The typical customer is parked for  hours.

c. Find the mean and standard deviation of the amount charged. (Round the final answers to 2 decimal places.)

Mean            

Standard deviation