+1-415-315-9853

info@mywordsolution.com

## Statistics

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?

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

### Please explain every step to make the sum understandableit

Please explain every step to make the sum understandable. It has been hypothesized that the distribution of seasonal colds in Canada is as follows: Season          Percentage Fall                    35% Winter            ...

### Mimi joined umuc basketball team since summer 2016 on

Mimi joined UMUC basketball team since summer 2016. On average, she is able to score 30% of the field goals. Assume she tries 15 field goals in a game. (a) Let X be the number of field goals that Mimi scores in the game. ...

### 1 distinguish between theory model and hypothesis2 describe

1. Distinguish between theory, model, and hypothesis. 2. Describe how researchers use induction versus deduction to generate research hypotheses. 3. Describe the process by which hypotheses are developed and tested.

### Questions1 the following results were observed in a

QUESTIONS: 1. The following results were observed in a prospective study of the drug Viagra (based on data from Pfizer Inc.)  Use the data to answer the following questions:   Viagra Treatment Placebo Headache 117 29 No ...

### 1 what is the name of the statistic used in an anova2 if

1. What is the name of the statistic used in an ANOVA? 2. If the independent variable has no effect, the calculated value of F will be around 1.00. Why?

### Problem 1 part i hypothesis testingconduct a one-tailed

Problem 1: PART I. HYPOTHESIS TESTING Conduct a one-tailed hypothesis test given the information below. A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shel ...

### Suppose that a ge 3 and let f be a social welfare function

Suppose that |A| ≥ 3, and let F be a social welfare function satisfying the properties of unanimity and independence of irrelevant alternatives. What are all the decisive coalitions?

### The umuc minimart sells five different types of coffee mugs

The UMUC MiniMart sells five different types of coffee mugs. The manager reports that the five types are equally popular. Suppose that a sample of 500 purchases yields observed counts 110, 100, 110, 100, and 80 for types ...

### In a random sample of 10 reduced fat chocolate chip cookies

In a random sample of 10 reduced fat chocolate chip cookies, the sample mean for the number of chocolate chips was 17.6.  Regular chocolate chip cookies have a mean number of 20 chocolate chips.  The population standard ...

### An individual wanted to determine the relation that might

An individual wanted to determine the relation that might exist between speed and miles per gallon of an automobile. Let X be the average speed of a car on the highway measured in miles per hour and let Y represent the m ...

• 13,132 Experts

## 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.

### 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