Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Statistics and Probability Expert

problem 1: For each of the statements below, prepare down whether it is true or false.

i) We are conducting a 2 tailed hypothesis test at a 1% significance level to test that the mean of a population is 500 against the alternative hypothesis that the mean is not the same. The correct null and alternative hypotheses are:

Ho : x‾ = 500 HA : x‾ ≠ 500.

ii) An experiment involves testing whether international soccer players are different in height from the rest of the population. A type II error in a two tailed-test for this problem would conclude that soccer players are the same height as the rest of the population when they are not.

iii) When using the p-value to test hypotheses, the decision rule depends only on the level of significance of the test.

iv) The standard error of the mean will increase when the sample size is increased.

v) As long as a sample is large enough, the shape of a sampling distribution of the sample proportion is approximately normal.

vi) We are using a t-test to test a hypothesis about a population mean. The degrees of freedom of the critical value depend on the sample size.

vii) The estimate of the standard error of an unknown population proportion is √(pq)/n

viii) The data collected by means of a survey are described as primary data.

ix) Simple random sampling is the method for obtaining the sample used to conduct the Australian Census.

x) The difference between a sample mean and the population mean arises from sampling errors only.

problem 2:

a) A beverage company uses a machine to fill its 500 ml cartons. The machine is calibrated to fill the cartons with an average of 505 ml and a standard deviation of 5 ml.
 
i) A  carton is randomly selected from a day’s production, what is the probability that it has been under filled?

ii) A random sample of 50 bottles is taken from a day’s production. What is the probability that the average fill volume is less than 500 ml?

iii) Based on your answers to part (i) and part (ii), what comment could be made about the company’s calibration standard?

problem 3:

Many consumers use credit cards for their convenience. A sample of 100 credit card holders finds that only 35% of them pay the card off each month.

a) Construct a 95% confidence interval estimate of the true proportion of credit card holders who pay off their credit cards each month.

b) Use the appropriate Excel workbook from Estimators.xls to construct a 99% confidence interval estimate of the proportion of credit holders who pay off their credit cards each month. Include the resulting Excel output with your answer. Highlight the upper and lower limits of the confidence interval in this output.

c) Which of the intervals in parts a. and b. is wider? prepare a sentence to describe why this is.

problem 4

a) A major bank is evaluating its recently revamped online banking system. Management will conclude there to be a problem with the system if less than 95% of users are satisfied with the service. 3000 customers were contacted but only 1568 agreed to be surveyed. Of these, 1452 were satisfied with the service they received. Do the sample data provide sufficient evidence to conclude that management has a problem with the online banking system? Use α = 0.05

State clearly the null and alternative hypotheses, the test statistic, test result, decision rule and conclusion in terms of the original problem.

b) What is the approximate p-value of the test in part a.? No working required.

c) How could this p-value be used to formally test the same hypotheses described in part a.? Just include the decision rule and the conclusion and a justification for the conclusion.

d) Suppose we wish to estimate the percentage of customers who are satisfied with the service to within 1%, within 95% confidence. What sample size would be required? Use the sample proportion from part a. when calculating the appropriate sample size.

problem 5:

A simple random sample of the birth weights of 100 babies in a major teaching hospital gave a mean weight of 3567 gm with a standard deviation of 492 gm. 

a) Construct a 99% confidence interval estimate of the population mean birth weight of babies born in this hospital.

b) Use the appropriate Excel workbook from Estimators.xls to construct the same interval as was required in part a. Include the resulting Excel output. Highlight the upper and lower limits of the confidence interval in this output. 

Note: This should provide a check of your calculations in part a. If there are big differences you should check both your manual calculations and your Excel calculations to determine where the error has occurred. 

problem 6:

An importer of women’s tracksuits needs to check that the average height of adult female basketball players is still 170cm. The company measures the heights of a random sample of 60 basketball players and finds the mean to be 175.4cm. Assume that the historic value for the standard deviation of 85.2 cm is unchanged.
 
a) Using a 0.05 level of significance, is there evidence that the heights of adult female basket ballers has changed?
 
State clearly the null and alternative hypotheses, the test statistic, test result, decision rule and conclusion in terms of the original problem.

b) Use the appropriate Excel macro in Test Statistics.xls to again perform the hypothesis test in part a. Present the output generated by Excel as your answer here. 

c) describe how this output verifies your conclusion in part a. by reference to either z-stat and z-critical or the p-value of the test. 

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M9645

Have any Question? 


Related Questions in Statistics and Probability

The centers for disease control and prevention released a

The Centers for Disease Control and Prevention released a report in 1998 that attributed part of the increase in youth smoking in the 1980s to the use of the cartoon character, Joe Camel, in cigarette advertising. Using ...

In a normal distribution what percentage of scores fall

In a normal distribution, what percentage of scores fall between -1 and +1 standard deviations from the mean? Between the mean and -2 standard deviations ? Between the mean and +3 standard deviations?

Onenbspstudy based on responses 1014nbsprandomly

One study, based on responses 1,014 randomly selected teenagers, concluded that 39% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of a ...

What three criteria must be met to establish that one

What three criteria must be met to establish that one variable causes changes in behavior? Which of these criteria are met by quasi-experimental designs? Which of these criteria are not met, and why?

In a manufacturing process a random sample of 36 bolts

In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt? Please s ...

Jullian was curious if regular excise really helps weight

Jullian was curious if regular excise really helps weight loss,she decided to perform a hypothesis test. A random sample of 5 Kansas State students was chosen. The students took a 30-minute exercise every day for 6 month ...

Given the following waiting time distribution in a hotel

Given the following waiting time distribution in a hotel, compute the  expected value  of the waiting time in 2 dec pl.    Waiting time (minutes) Probability 4.0            20% 4.5 28% 5.0 32% 5.5 10% 6.0 10%

Suppose we randomly sample 400 nucleotides from the human

Suppose we randomly sample 400 nucleotides from the human genome. (Consider only a single strand.) Does the occurrence of adenine, thiamine, cytosine and guanine (A, C, T and G) in this sample suggest that nucleotides in ...

Imagine that the equation for predicting y from x is y 112

Imagine that the equation for predicting y from x is y = 1.12 - .47x. How would you use this equation to predict a particular individual's score?

Question 1use this extract taken from the article goji

Question 1: Use this extract taken from the article, "Goji berries prevent macular degeneration," (appeared in Healthy Foods, Healthy Bodies on January 21, 2016) to answer the questions that follow: Goji berries (Lycium ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen