Assume that a simple random sample has been selected and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Listed below are brain volumes in cm3

of unrelated subjects used in a study. Use a 0.05

significance level to test the claim that the population of brain volumes has a mean equal to

1099.2cm3.

A medical researcher says that less than

2323​%

of adults in a certain country are smokers. In a random sample of

200200

adults from that​ country,

16.516.5​%

say that they are smokers. At

alphaαequals=0.050.05​,

is there enough evidence to support the​ researcher's claim? Complete parts​ (a) through​ (e) below.​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

What is the​ claim?

A.Less than

2323​%

of all adults are smokers.

B.Less than

2323​%

of adults in the country are smokers.

C.Exactly

16.516.5​%

of all adults are smokers.

D.Exactly

16.516.5​%

of adults in the country are smokers.Identify

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0H0​:

p

▼

greater than>

greater than or equals≥

less than or equals≤

less than<

nothing

Upper H Subscript aHa​:

p

▼

greater than or equals≥

not equals≠

less than or equals≤

less than<

greater than>

nothing

​(Type integers or​ decimals.)

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

The critical​ value(s) is/are

z 0z0equals=nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What​ is/are the rejection​ region(s)? Select the correct choice below and fill in the answer​ box(es) to complete your choice.

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

A.

zless than<nothing

and

zgreater than>nothing

B.

zgreater than>nothing

C.

zless than<nothing

​(c) Find the standardized test statistic z.

zequals=nothing

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

​(d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

▼

Fail to reject

Reject

Upper H 0H0.

There

▼

is not

is

enough evidence at the

55​%

level of significance to

▼

support

reject

the​ researcher's claim that

▼

less than 23%

exactly 16.5%

of

▼

adults in the country

all adults

are smokers.

Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of patients with SAD to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)

State the decision for the main effect of the time of day.

Retain the null hypothesis.Reject the null hypothesis.     

State the decision for the main effect of intensity.

Retain the null hypothesis.Reject the null hypothesis.     

State the decision for the interaction effect.

Retain the null hypothesis.Reject the null hypothesis.     

Summarize the results for this test using APA format.

Calculate the sample standard deviation and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Class Frequency
61 - 66 4
67 - 72 8
73 - 78 5
79 - 84 7
85 - 90 13

1. A racing team owner wants to attempt to qualify his car for a major auto race. The owner believes that it will take a mean qualifying speed of over 223 mph to qualify for the race. During the two days of testing prior to qualifying, the team conducted 10 practice qualifying runs. The mean speed of these qualifying runs was 224.5 mph, with a standard deviation of .75 mph. Based on this information, does the owner have reason to believe that his car will qualify for the race, with at least 95% confidence. Assume all normality conditions apply. Solve using the p-value approach.

1. State the null hypothesis

2. State the alternative hypothesis

3. State the significance level.

4. Perform the calculations.

Suppose you are tossing a fair coin. You will keep tossing until you get two consecutive
heads. Let, X represents the number of tosses you will need. So the minimum value of X is
two.
(a) Using hand calculation, calculate P[X = 2], P[X = 3], P[X = 4] and P[X = 5].
(b) How to write an R function that keeps tossing the fair coin until two consecutive heads
show up and returns the total number of tosses. (run this function 1000 times)

Andrew surveyed a random sample of 500 Honolulu citizens on their attitudes toward legalizing marijuana use on a 7-point scale (1 strongly oppose, 4 neutral, 7 strongly support). The mean response of this sample of respondents is 4.4, and standard deviation (SD) is 2.5.

Assume that 4 indicates a neutral attitude. Can Andrew can claim that Honolulu citizens are on average in favor of legalizing marijuana use at 95% confidence level?

A 2007 Carnegie Mellon University study reported that online shoppers were willing to pay, on average, more than an extra $0.60 on a $15 purchase in order to have better online privacy protection.
A sample of n=22n online shoppers was taken, and each was asked how much extra would you pay, on a $15 purchase, for better online privacy protection?'' The data is given below, in $'s.

0.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.500.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.50

(a) Do the data follow an approximately Normal distribution? Use alpha = 0.05.  ? yes no

(b) Determine the PP-value for this Normality test, to three decimal places.
P=

(c) Choose the correct statistical hypotheses.
A. H0:μ=0.60HA:μ>0.60H0:μ=0.60HA:μ>0.60
B. H0:X¯¯¯¯=0.60,HA:X¯¯¯¯<0.60H0:X¯=0.60,HA:X¯<0.60
C. H0:μ>0.60HA:μ=0.60H0:μ>0.60HA:μ=0.60
D. H0:X¯¯¯¯=0.60,HA:X¯¯¯¯>0.60H0:X¯=0.60,HA:X¯>0.60
E. H0:μ=0.60,HA:μ≠0.60H0:μ=0.60,HA:μ≠0.60
F. H0:μ>0.60,HA:μ<0.60H0:μ>0.60,HA:μ<0.60


(d) Determine the value of the test statistic for this test, using two decimals in your answer.
Test Statistic =
(e) Determine the P-value for this test, enter your answer to three decimals.
P=

(f) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use alpha = 0.05

According to a PARADE poll of 1200 Americans, 75% of the respondents claimed that they had changed their behavior I an attempt to lower their risks of heart disease.  Assume that these 1200 people represent a random sample.  

a.) find a 98% confidence interval for the percentage of all Americans who say that they have changed their behavior to lower their risks of heart disease.

15. A researcher wants to know the poverty rate for the state of Kansas. The researcher randomly selects 150 families and finds 25 are at or below the poverty line.

a) Determine a 95% confidence interval for the proportion. State this interval below within an interpretive sentence tied to the given context.

b) The poverty rate for the US is stated to be 12.3%. Is there evidence at the 95% confidence level that the the poverty rate is higher than 12.3%? Explain your reasoning.

Explain the statistical concept of regression or reversion to the mean and provide an example.

A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Identify the simple events comprising the event (A and B). Select one: {1, 2, 3, 4, 5, 6} {2, 4, 6, 8, 10} IncorrectIncorrect {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} {2, 4, 6} Question 10 Incorrect 0.00 points out of 1.00 Not flaggedFlag question Question text A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Identify the simple events comprising the event (A or B). Select one: {1, 2, 3, 4, 5, 6, 8, 10} {1, 2, 3, 4, 5, 6, 7, 8, 10} {1, 2, 3, 4, 5, 6} IncorrectIncorrect {2, 4, 6}

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Do you take the free samples offered in supermarkets? About 64% of all customers will take free samples. Furthermore, of those who take the free samples, about 41% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 309 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?


(b) What is the probability that fewer than 200 will take your free sample?


(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample) = 0.41, while P(sample) = 0.64.


(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use the probability of success calculated in part (c).

Prob 1Coffee Beanery in Chicago  is open 365 days a year and sells an average of 120 pounds of Kona Coffee beans a day (Assume demand is to normally distributed with a standard deviation of 40 pounds/day). Beans are ordered from Hawaii, and will arrive in exactly 4 days with a flat rate shipping and handling charge of $150. Per-pound annual holding costs for the beans are $3. Coffee is highly profitable, so the Beanery would like to have at most a 1% chance of running out of beans. Orders should be placed in whole pounds, but otherwise the Kona suppliers can deal with orders of any size. .

1)Calculate the economic order quantity (EOQ) for Kona coffee beans ________lbs

2)Calculate the total annual holding costs of cycle stock for Kona coffee beans $__________

3) Calculate the total annual fixed ordering costs for Kona coffee beans $__________

4)Calculate the Re-Order Point ________lbs

5)If management specified that a 2% stock-out risk is now okay, would safety stock holding costs decrease, increase, remain unchanged or do we not have enough info to tell? (Circle 1)

Problem 1-contd' Now assume that Kona supplier wants to place the Beanery on a fixed order intervals, where they will only deal with orders every 3 weeks (Hawaiians have better things to do than be waiting by the phone for obnoxious Manhattanites). Assume all other parameters remain the same.

1)If the Beanery has only 350lbs of beans left on the day they are allowed to place an order, calculate the probability they will run out before this next order arrives. ________%

2)Compare the cost of safety stock for the Fixed Order interval to that associated with the reorder point. How does it differ and why?

A sample of final exam scores is normally distributed with a mean equal to 20 and a variance equal to 25. a) what percentage of scores is between 15 and 25. b) what raw score is the cutoff for the top 10% of scores. c) what is the probability of a score less than 27. d) what is the proportion below 13.