Question 1
You are advised to first perform the appropriate hypothesis test using pencil and paper, along with a calculator and statistical tables, and then use your working to answer the questions below.
An administrator at a medium-sized hospital tells the board of directors that, among patients received at the Emergency room and eventually admitted to a ward, the average length of time between arriving at Emergency and being admitted to the ward is 4 hours and 15 minutes. One of the board members believes this figure is an underestimate and checks the records for a sample of 25 patients.
The sample mean is 6 hours and 30 minutes. Assuming that the population standard deviation is 3 hours, and that the length of time spent in Emergency is normally distributed, use the sample data to determine whether there is sufficient evidence at the 5% level of significance to assert that the administrator's claim is an underestimate?
(NOTE: Convert all times to hours (as a decimal) before completing calculations. For example 3 hours and 20 minutes = 3 hours + 20/60 = 2.33 hours )
(a) According to the null hypothesis, the value of the population mean is hours. (Give your answer in hours to 3 decimal places x.xxx (Answer in hours not in hours and minutes)
(b) Is the test one-tailed or two-tailed?
(c) To 3 decimal places the critical value of the test statistic for this hypothesis test is:
(d) To 3 decimal places the test statistic calculated from the sample is:
(e) Is the null hypothesis rejected at the 5% level?
(f) Does this indicate that the average time spent in the Emergency Room has changed?
(g) Is the assumption that the time in the Emergency Room is normally distributed necessary in order to perform this test?
Question 2
You are advised to first perform the appropriate hypothesis test using pencil and paper, along with a calculator and statistical tables, and then use your working to answer the questions below.
The administrators of a medium-sized hospital are gathering data to help in the planning of upgrades to various parts of the hospital. In determining whether the capacity of the Emergency Room is appropriate, one question is, among patients received at the Emergency room and eventually admitted to a ward, what is the average length of time between arriving at Emergency and being admitted to the ward? Last time similar planning documents were prepared, this length of time was known to be 5 hours and 15 minutes. To check whether this figure has changed, the records are accessed for a sample of 25 recent patients. The sample mean is 6 hours and 30 minutes. Assuming that the population standard deviation is 3 hours, and that the length of time spent in Emergency is normally distributed, use the sample data to determine whether there is sufficient evidence at the 5% level of significance to assert that the old value should be changed.
(a) According to the null hypothesis, the value of the population mean is hours. (Give your answer in hours to 2 decimal places x.xx (answer in hours not in hours and minutes))
(b) Is the test one-tailed or two-tailed?
(c) To 3 decimal places the positive critical value of the test statistic for this hypothesis test is:
(d) To 3 decimal places the test statistic calculated from the sample is:
(e) Is the null hypothesis rejected at the 5% level?
(f) Does this mean that the hospital administrator provided accurate information to the board?
(g) Is the assumption that the number of beds filled is normally distributed necessary in order to perform this test?
Question 3
The p-value criterion for an hypothesis test with significance level alpha is to reject the null hypothesis if
Select one:
a. p-value = alpha
b. p-value < alpha
c. p-value > alpha
d. -alpha < p-value < alpha
If we reject the null hypothesis, we conclude that
Select one:
a. there is enough statistical evidence to infer that the null hypothesis is true
b. there is enough statistical evidence to infer that the alternative hypothesis is true
c. there is not enough statistical evidence to infer that the alternative hypothesis is true
d. the test is statistically insignificant at whatever level of significance the test was conducted at
A Type II error is committed if we make:
Select one:
a. a correct decision when the null hypothesis is false
b. A correct decision when the null hypothesis is true
c. an incorrect decision when the null hypothesis is false
d. an incorrect decision when the null hypothesis is true
You are advised to first perform the appropriate hypothesis test using Excel and pencil and paper, along with a calculator and statistical tables where appropriate, and then use your working to answer the questions below.
Many overseas sellers using online auction platforms such as Ebay provide an estimate for the number of days a package will take to arrive at a particular destination country from the time of order. A random sample of the time taken for a package to arrive in Australia from the time of ordering from a seller based in Hong Kong was obtained. The data in the Excel file A4_S2_2014.xls represent the number of days taken for a package to arrive from the overseas seller.
The seller claims that the mean number of days for a package to arrive in Australia is 13 days or less. Does the sample data obtained provide evidence that the mean arrival time for packages is as the seller claims at the 5% level of significance? Formulate null and alternative hypotheses regarding the data, and explain why the choice of null and alternative hypotheses is appropriate. (Remember we are
seeking evidence that the claim made by the seller is not true).
Give the following statisitcs for this data. Complete required working using Excel first.
Population mean (H):
. (Give your answer as a whole number in the form xx).
Sample mean (x_bar):
. (Give your answer as a whole number in the form xx).
Sample standard deviation (s):
. (Give your answer to three decimal places in the form x.xxx).
Sample size (n):
. (Give your answer as a whole number in the form xxx).
Level of significance (alpha a):
. (Give your answer as a proportion to two decimal places in the form xxx).
Complete the two hypotheses which describe this situation
Null Hypothesis Ho: p =
. (Give your answer here as a whole number in the form xx).
Alternative Hypothesis Ha:
. (In the first box insert the appropriate symbol <, > OR. For the second box give your answer here as a whole number in the form xx)
What distribution do the sample means follow in this case?
. (Type Z or t).
Is this distribution associated with a number of degrees of freedom?
. (If Yes, give the appropriate number of degrees of freedom as a whole number in the form xxx or else type NO)
Calculate the value of the test statistic for this set of data:
. (Give your answer to three decimal places in the form x.xxx).
Give the critical value for the test at 5% level of signifcance:
. (Use Excel to find this value. Give your answer to three decimal places in the form x.xxx}
What is the p-value for the test?
. (Use Excel to find this value. Give your answer to three decimal places in the form x.xxx. If its in scientifc notation don't forget to change it to a decimal first}
What is your decision about the hypotheses:
the Null Hypothesis. (Type ACCEPT or REJECT).
And hence the Alternative Hypothesis. (Type ACCEPT or REJECT).
A series of statements ragarding the evidence you used to make this decision are given below. For each statement type TRUE or FALSE.
We rejected the null hypothesis because the test statisitc was greater than the critical value. We did not reject the null hypothesis because the test statistic was greater than the critical value.
The p-value is less than the level of signifcance so we reject the null hypothesis.
The p-value is greater than the level of significance so we do not reject the null hypothesis.
We conclude that the claim by the seller that the mean number of days taken for apackage to arrive is 13 days or less been supported by the data. (Type HAS or HAS NOT).