Statistics-QA27

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Problem 1
 
The amount of time a customer waits for service at a bank is normally distributed. While the manager believes that the waiting time for customers is at most 3 minutes on average, a customer claims that the average waiting time is at least 3.5 minutes. You selected a random sample of 16 customers and obtained a mean of 3.10 minutes and a standard deviation of 0.40 minutes for their wait times.
 
a) Write your null and alternate hypotheses to test the manager’s belief (i.e., the waiting time for the customers is at most 3 minutes on average).
b) Using a significance level of 0.05, test the above hypotheses and draw your conclusion using a critical value (classical method) approach.
c) Test the customer’s claim (i.e., the average waiting time is at least 3.5 minutes) and draw your conclusion about the claim using 𝛼=0.10.
 
Problem 2
 
The owner of a gas station wants to study gasoline purchasing habits of motorists at his station. He selects a random sample of 60 motorists during a certain week, with the following results
 
• The average amount purchased was = 42.78 liters,
• Standard deviation = 11.73 liters
• 11 motorists purchased premium-grade gasoline.
 
a) At the 0.05 level of significance, is there evidence that the mean amount purchased was differed significantly from 38 litres?
b) Determine the p-value in (a).
c) At the 0.05 level of significance, is there evidence that fewer than 20% of all the motorists at the station purchased premium-grade gasoline?
d) What is your answer to (a) if the sample mean equals 40 liters?
 
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Problem 3
 
A random sample of 250 business faculty members was asked if there should be a required foreign language course for international business majors. Of these sample members, 170 felt there was a need for a foreign language course.
 
a) State your hypothesis to test whether there is significant evidence that at least 75% of all business faculty members hold this view.
b) Test your hypothesis using 𝛼=0.01 and state your conclusion.
 
Problem 4
 
A product is produced by two different machines. Two random samples were selected, and the following summary information were computed accordingly
 
Machine 1
Machine 2
Sample size
80
100
Sample mean
4.5 gm
4.4 gm
Population standard deviation
0.5 gm
0.6 gm
 
a) Estimate the confidence interval of the difference between the two means with 80% confidence level.
b) What are the assumptions you considered for the above solution?
 
product code: Statistics-QA27
 
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