Search & Filtering
A population consist of the four numbers 1, 2, 4 and 5. List all the possible samples of size n=3 which can be drawn with replacement from population
a. Test if the proportion of unemployed non-science male graduates is 5 percent less than the proportion of unemployed science male graduates at 10 percent significance level.
i) Specify the competing hypotheses of the test (2 Marks)
ii) Calculate the value of the relevant test statistic (4 Marks)
The area under the standard normal curve where p( 0 < z < 1.31)
two types of fibers are suitable for use by a fish net manufacturer. the breaking strength of this fabric is important. it is known that "\\sigma"1="\\sigma"2=1.0 psi. from random samples of n1=10 and n2=12 we obtain y1=162.5 and y2= 155.0. the company will not adopt fiber 1 unless its breaking strength exceeds that of fiber 2 by at least 10 psi. based on the sample information, should they use fiber 1? in answering this question, set up and test appropriate hypotheses using "\\alpha"=0.01. construct a 99 percent confidence interval on the true mean difference in breaking strength.
Two types of fibers are suitable for use by a fish net manufacturer. the breaking strength of this fabric is important. it is known that "\\sigma"1="\\sigma"2=1.0 psi. from random samples of n1=10 and n2=12 we obtain y1=162.5 and y2= 155.0. the company will not adopt fiber 1 unless its breaking strength exceeds that of fiber 2 by at least 10 psi. based on the the sample information, should they use fiber 1? in answering this question, set up and test appropriate hypotheses using "\\alpha"=0.01. construct a 99 percent confidence interval on the true mean difference in breaking strength.
N&M magazine believes that it has a 38% share of the national female readership market of women’s magazines. When 2 000 readers of women’s magazines were randomly selected and interviewed, 700 stated that they read N&M regularly.
(3)
2.1.1Does the sample evidence support their claim? Explain.(5)
2.1.2 What is the population of interest in this case?(2)
2.1.3What is the sample in this case?
(2)
2.1.4 What percentage of readers interviewed read N&M magazine regularly? Is this a statistic or a parameter? Explain.
2.1.5 What does the value 38% represent in the above case? Explain.
A fair dice is cast what’s the probability that
(a)the result is 4
(b)the result is odd
The accountant for Lane and Company uses a statistical control chart to help management to decide when to investigate variances. The critical value is one standard deviation from the mean. The company incurred the following direct labour efficiency variances during the first six months of the year:
January
$500 F
April
$1800 U
February
1600 U
May
2100 U
March
1400 U
June
2400 U
The standard direct labour cost during these months was $36000.
Required
1. Suppose that the accountant’s rule of thumb is to investigate all variances equal to or greater than 5 percent of standard direct labour cost. Which variances will be investigated?
Would you investigate any of the variances listed above other than those indicated by the rules discussed in requirement 1? Explain your answer.
Sales personnel for X Company are required to submit weekly reports
listing customer contacts made during the week. A sample of 61 weekly contact
reports showed a mean of 22.4 customer contacts per week for the sales personnel.
The sample standard deviation was 5 contacts.
1. Develop a 95% confidence interval estimate for the mean number of weekly
customer contacts for the population of sales personnel.
2. Assume that the population of weekly contact data has a normal distribution.
Use the t distribution to develop a 95% confidence interval for the mean number
of weekly customer contacts.
3. Compare your answer for parts (a) and (b). What do you conclude from your
results?
A factory manufacturing light-emitting diode (LED) bulb claims that their light bulbs last for 50,000 hours on the average. To confirm if this claim was valid, a quality control manager got a sample of 50 LED bulbs and obtained a mean lifespan of 40,000 hours. The standard deviation of the manufacturing process is 20,000 Do you think the claim of the manufacturer is valid at the 5% level of significance?
