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The average length of time for student to register summer classes at a certain university has been 50 minutes with a standard deviation of 10 minutes. A new registration procedure using modern computing machine is being tried. If a random sample of 12 students had a n average registration of 42 minutes with a standard deviation of 11.9 minutes under the new system, test the hypothesis that the population mean is now less than 50 minutes. (critical value is +/- 1.796)
A population consists of the elements 3, 5, 7, 8, and 10. What is the population variance?
Round off your answer to the nearest hundredths.
Solve the given problems
1. A population consists 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 the population
Find the following
a Population mean
b. Population variance
c. Population standard deviation
d. Mean of the sampling distribution of sample means
e. Variance of the sampling distribution of sample means
f Standard deviation of the sampling distribution of sample means
A sushi store offers 10 flavors of sushi and 3 types of sashimi. How many combinations of sushi and sashimi can a customer choose from?
5. A teacher wants to test his assumption that less than 30% of the Senior High
School students liked research class. After randomly collecting 150 samples,
he found out that only 40 students like their research class.
Claim:
Parameter
Symbol for parameter
Ho and Ha complementary pair.
Hypotheses in words:
Ho
Ha:
Hypotheses in symbols
Ho
На:
3. The Senior High School researchers claim that more than 20% of Senior High
School male students have tried smoking cigarette. After collecting 150 random
samples, they found that 60 of them have tried smoking cigarette.
Claim:
Parameter
Symbol for parameter
Ho and Ha complementary pair.
Hypotheses in words:
Ho
Ha:
Hypotheses in symbols
Ho
На:
4. In a certain town a school principal hypothesized that students enroll in schools
within 5 km from their homes. To check this claim you ask 38 students from
the said town. You found out that the average distance between the students
home and their schools is 5.6 km.
Claim:
Parameter
Symbol for parameter
Ho and Ha complementary pair.
Hypotheses in words:
Ho
Ha:
Hypotheses in symbols
Ho
На:
What is the probability that, for the sample of 115 customers, the proportion who wait longer than five days for their order to be delivered is less than 13.75%? Interpret your answer
A shop owner claims that on average, his shop has a daily turnover of R75 000. Test this claim at the 5% significance level, if the average daily turnover for a sample of 88 days was R71 500. Assume a population standard deviation of R4 450.
The CEO of Global Investment Funds claims that, on average, clients leave their investment funds with the company for a period of at least 56 months. Test this claim at the 10% significance level, if it was found that a sample of 29 clients left their investment funds with the company for an average period of 58.85 months, with a standard deviation of 3.75 months
A large manufacturing company claims that more than 88% of its customers are fully satisfied with the company’s products. Test this claim at the 5% significance level, if a survey found that 360 out of a random sample of 400 of the company’s customers said that they were fully satisfied with the company’s products.
