Statistics and Probability Answers

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.

Given the following information, construct the rejection region. Show the solution in

a step-by-step procedure.

H 0 : = 45

H a : < 45

= 40, = 12, n = 32, = 0.01

II. Determine if one-tailed test or two-tailed test fits the given alternative hypothesis.

1. The mean height of Grade 12 students is less than 66 inches.

Answer: ___________________________

2. The standard deviation of their height is not equal to 5 inches.

Answer: ___________________________

3. Male Grade 7 and Grade 12 students differ in height on average.

Answer: ___________________________

4. The proportion of senior male students’ height is significantly higher than the senior female students.

Answer: ___________________________

5. The average grade of Grade 11 students in Statistics is lower than their average grade in Calculus.

Answer: ___________________________