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

You are offered the right to receive 3000 per year forever

You are offered the right to receive 3,000 per year? forever, starting in one year. If your discount rate is 3?%, what is this offer worth to? you? (round to the nearest dollar)

An important part of the customer service responsibilities

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a ...

An aerospace company has submitted bids on two separate

An aerospace company has submitted bids on two separate federal government  defense contracts, AandB . The company feels that it has a 60% chance of winning contract Aand a 30% chance of winning contractB . If it wins co ...

What is the sample size for studies with moe of -35 and -28

What is the sample size for studies with MOE of +/-3.5% and +/-2.8%, with a confidence level of 95%, sample statistics of 50. Suppose the category population was 7500 (less than 10,000)? Remember the FPC. What would be t ...

A company that supplies batteries for watches guarantees

A company that supplies batteries for watches guarantees that 95% of the batteries it ships will be free from defects. You test a sample of 50 batteries you received. You find that fewer than 10 have defects. Does this l ...

Future value of an annuitywhat is the future value of a 470

Future Value of an Annuity What is the future value of a $470 annuity payment over 7 years if the interest rates are 6 percent?

The distribution of actual weights of 8-oz chocolate bars

The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.7 ounces and standard deviation 0.2 ounces. a) What is the probability that the average weight of a random sam ...

Would you actually build a contingency chart for this

Would you actually build a contingency chart for this question or is this just probability basics? Bob sets two battery powered alarm clocks to make sure he wakes up in time for his 8 AM accounting test. Each alarm clock ...

Two candidates face each other in an election the

Two candidates face each other in an election. The Democratic candidate is supported by 58% of the population, and the Republican candidate is supported by 42%. In other words, if you randomly chose a voter and asked the ...

The dow jones industrial average has had a mean gain of 432

The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 years is selected. What is the probability that the mean gain for the sample was between 200 a ...

  • 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

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As