Reserve Problems Chapter 8 Section 2 Problem 2

During the nutrition research, the amount of consumed kilocalories per day was measured for 18 people – 10 women and 8 men. Results are as follows:

Women: 1962, 1842, 1588, 1911, 1779, 1603, 1758, 1771, 1874, 1974;

Men: 2097, 2560, 2328, 2399, 2420, 2292, 2263, 2047.

Calculate a 90% confidence interval on the mean for women and men separately. Assume distribution to be normal.
Round your answers to the nearest integer (e.g. 9876).

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective.

Step 2 of 2:

Suppose a sample of 1996 floppy disks is drawn. Of these disks, 319 were defective. Using the data, construct the 99% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Question 2: The American Journal of Clinical Nutrition published the results of a study of the dietary intake of sugar by children.

In the trial a sample of 657 randomly selected American children between the ages of 5 and 12 was chosen, and for each child a seven day food diary was filled in. An analysis of the data showed a sample mean of 134.3 g of sugar per day with a standard deviation of 48.1 g. Using the results from this sample, estimate the 68%, 95%, and 99% confidence intervals for the mean daily sugar intake of all American children (i.e., the population mean).

Please provide
Definitions, some explanation along with example for each topic
(Note: please provide all data in text format pdf/text so i can copy into MsWord because i have to submit my assignment in printed form)

1)Random experiment
2)properties of random experiment
3)sample space
4)event
5)simple event
6)compound event
7)equally likely event
8)mutually exhaustive probability
9)classical or priori probability
10)relative frequency or posterior prob.
11)Axiamatic probability
12) Properties of probability

In Caribbean seagrass meadows manatee grass Syringodium filiforme appears before turtle grass Thalassia testudinum. (a) Describe the design of an experiment to determine the mechanism of this successional sequence. (b) Give the statistical null hypothesis for this experiment.

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. and Compute the mean of this general discrete probability distribution. ( 6 marks)
2. Compute the standard deviation of this general discrete probability distribution. ( 5 marks)
3. What is the probability that exactly 4 televisions will be sold on any given day? and What is the probability that 2 or more televisions will be sold on any given day? ( 2 mark)
4. What is the probability that less than 2 televisions will be sold on any given day? and What is the probability that between 1 and 4 televisions inclusive will be sold on any given day? (2 mark)

Paired Samples t-test

Gregg Popovich, head coach of the San Antonio Spurs, had his top five scorers practice during the past week with the shooting coach Chip Engelland. They shot 100 free throws prior to working with Chip and then shot 100 free throws after working with Chip. Below are the total number of free throws made before and after working with Chip Engelland. Popovich wants to know if practicing with Chip increased their free throw making abilities. Use a p-value (α) of 0.05 to conduct the test.

Step 1: Populations, Distribution, and Assumptions

Population 1:

Population 2:

Distribution:

Hypothesis test to be used (Explain):

Step 2: Hypotheses

Research Hypothesis:

Symbolic Research Hypothesis:

Null Hypothesis:

Symbolic Null Hypothesis:

5

Step 3: Characteristics of the Comparison Distribution (6 points)

Um (mean of means) = __________

SM= __________

Step 4: Critical Values

t critical, =____________-.

df= __________

Step 5: Calculate Test Statistic

t statistics =____________

Step 6: Make a Decision

Be sure to explain and also report your answer in APA format.

SS =________________

6

Effect Size

Calculate the effect size for the previous comparison. Cohen’s d = __________

Confidence Interval

Calculate the confidence interval

CI 90% = [ ________ , _________ ]

QUESTION 2  

According to Michael Theatre Ltd., the mean cost to run a nightly theatre performance is $3,100 with a standard deviation of $440. Performance costs are known to follow a normal probability distribution.

Required:

1. What percentage of the performances will cost less than $2,850 to run? Sketch a normal curve and shade the desired area on your diagram. ( 4 marks)

2. What percentage of the performances will cost between $3,150 and $3,520 to run? Sketch a normal curve and shade the desired area of your diagram. ( 4 marks)

3. What percentage of the performances will cost between $2,300 and $3,520 to run? Sketch a normal curve and shade the desired area on your diagram. ( 4 marks)

4. What percentage of the performances will cost less than $3,750 to run? Sketch a normal curve and shade the desired area of your diagram. ( 4 marks)

5. Six percent (6 %) of all shows will cost less than what dollar amount? Sketch a normal curve and shade the desired area of your diagram. ( 4 marks)

Use the research described below to answer the questions that follow. Shargorodsky, Curhan, Curhan, and Eavey (2010) examined hearing loss data for participants from the National Health and Nutrition Examination Survey (NHANES), aged 12-19 years. (NHANES provides nationally representative cross-sectional data on the health status of the civilian, non-institutionalized U.S. population.) The researchers compared the more recent hearing loss rate among teens (12-19 years) in 2005 to previous levels in 1988. Their goal was to see whether teen hearing loss is increasing, possibly due to heavier use of ear buds. They examined data from 1771 participants in the NHANES 2005 study (333 with some level of hearing loss), as well as data on 2928 teens from the NHANES 1988 study, with 480 in this group showing some level of hearing loss.

QUESTION 1: Calculate the p-value

QUESTION 2: Calculate an appropriate confidence interval for the change (if it exists) in hearing loss.

An engineer wanted to estimate the true mean resistance of a certain electrical circuits (?) by a sample mean (?̅). It is known that the population is normal, and the population standard deviation is ? = 0.25 ohms. Determine the required sample size (?) so that he will be 90% confident of being correct within ± 0.06.

Chapter P, Section 1, Exercise 042

Pancakes

A friend makes three pancakes for breakfast. One of the pancakes is burned on both sides, one is burned on only one side, and the other is not burned on either side. You are served one of the pancakes at random, and the side facing you is burned. What is the probability that the other side is burned? (Hint: Use conditional probability.)

Enter the exact answer.

P(other side is burned): _____________________   0.5 and .67 both (Incorrect Answers)

0.5 (Incorrect Answer)

A survey was undertaken to estimate the hours worked per week by volunteers in a social service agency. The agency provides telephone support 7 days a week for 12 hours each day.

There are currently 12,478 volunteers across the country. This number is the number recorded in the volunteer register on 1 May 2018. 100 of these volunteers were randomly chosen. The 100 were each sent an email and asked to record the total hours they worked for the week starting on Monday 7^th May.

In this sample survey, what is the target population that is being sampled? What is the size of the population that is being sampled?

What is the sample unit in this survey? What is the size of the sample?

What is meant by the words “sample frame”? Use this study’s sample frame to explain your answer.

Describe in this study how the sample frame could by mistake include population units that are not in the target population.

Describe in this study how the sample frame could by mistake exclude population units that are in the target population.

Describe how you would randomly select the 100 volunteers for the survey.

What measurement are you taking from each sample unit?

What is the sample estimator in this survey?

Write down four examples of possible non-sampling errors in this survey.

If you were to improve the survey by using stratified random sampling, how would you create separate strata for this population (i.e. what information would you use to stratify the target population)?

Describe what stratified random sampling is and how in this situation it could improve the survey by reducing the variance of the sample estimator.

QUESTION 7

1. In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported by US Today). The claim is that cell phone users develop cancer of the brain or nervous system at a rate that is greater than the rate of 0.034% (0.00034) for people that do not use cell phones.

   Use this information to answer this question and the next five (5) questions.

   The 95% confidence interval for the true population proportion of cell phone users who develop brain or nervous system cancers is (lower confidence limit bound, upper confidence limit bound ).

QUESTION 8

1. What can you conclude by comparing the 95% Confidence Interval and the rate of cancer of the brain or nervous system for non-cell phone users? Justify your answer.

QUESTION 9

1. In performing a formal test of hypothesis to determine if the use of cell phones increases the rate development of the brain or nervous system cancers, the form hypotheses are:

   		Ho: Pu = 0.00034; Ha: Pu ≠ 0.00034
   		Ho: Pu = 0.00034; Ha: Pu > 0.00034
   		Ho: Pu > 0.00034; Ha: µ < 0.00034
   		Ho: Pa = 0.00034; Ha: Pa ≠ 0.00034

QUESTION 10

1. Using the cell phone brain and nervous system cancer rate information from above, find the appropriate critical standard normal z-value for performing the test of hypothesis.

QUESTION 11

1. Perform the formal test of hypothesis and obtain the z-calc value to see if using cell phones increases the rate of the development of the brain or nervous system cancers using the information from above.

QUESTION 12

1. Compare z-critical and z-calc and draw the appropriate conclusion for this test of hypothesis. Justify your answer.