Question 1145270: 2.1 What determines use of t-distribution and z-distribution in confidence interval calculation? [3]
2.2 A travel agency call Centre wants to know the average of calls received by its call Centre. A random sample of 21 days is selected and the sample mean number of calls received was found to be 166.2 with a sample standard deviation of 22.8 calls. Assume that calls received daily are normally distributed.
2.2.1 Calculate a 95% confidence interval for the mean number of daily calls received by the call Centre. [6]
2.2.2 Find the 99% confidence interval for the mean number of daily calls received by the call Centre. [6]
2.2.3 Compare the differences in in your answers in i & ii and briefly explain the cause. [3]
2.3 For a sample of 256 owners of medium-sized cars, it was found their average monthly car monthly car insurance premium for comprehensive cover was R356. Assume that the population standard deviation is R44 per month and that insurance premiums are normally distributed.
2.3.1 Find the 95% confidence interval for the average monthly comprehensive car insurance premium paid by all owners of medium - sized cars. [7]
QUESTION 3 (10 MARKS)
The lecturer claims that average percentage pass mark of a subject is 60% and the Head of Department is skeptic with this claim. To verify this claim the Head of Department sampled 76 scripts and discovered that 48 scripts were above the 60% mark.
REQUIRED:
Conduct a hypothesis to test this claim at 1% significance level. [10]
Can do 2-way test since I don't know which direction is likely
Ho: percentage = 60%
Ha: percentage NE 60%
alpha=0.01 P{reject Ho|Ho true}
test stat is a 2-way proportion with critical |z| > 2.576
48/76=0.63
z=(0.63-0.60)/sqrt(0.6*0.4/76); sqrt term =0.0562
=0.03/0.0562=0.5338. Fail to reject Ho, and the script percentage may be 60%. Insufficient evidence to show that it is not 60%.
QUESTION 4 (15 MARKS)
The operations manager of a company wants to compare the performance of two branches under his oversight. The manager wants to find out which branch is doing well.
A random sample of 18 orders from Gauteng branch had an average value of R335.20 with a standard deviation equal to R121.50. Orders received by Limpopo branch had 15 orders sampled were R265.60 with sample standard deviation of R152.20.
Can the operations manager conclude, at 10% significance level, that the Gauteng branch is performing better than the Limpopo branch? [15]
QUESTION 5 (25 MARKS)
A company produces labeled packaging material and the company intends to buy a new machine for shaping and labeling. The company has been approached by two different companies and the production manager did a test on these machines on processing times and obtained the following results.
Machine A (in minutes) Machine B (in minutes)
11 10
13 11
12 13
09 08
14 14
Can it be concluded that there is no difference in the mean processing time between the two different machines? Use α=0.10. Formulate the null and alternative hypotheses. Interpret the findings for the company. [25]
Answer by ikleyn(52863)   (Show Source):
You can put this solution on YOUR website! .
One and only one problem / question per post.
It is the rule and the policy of this forum.
Those who violate this rule, work against themselves.
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