Statistics and Probability Answers

If the sample size n=15, level of significance α=0.05, and a test design of two-tailed test, compute the critical t-value or the rejection region.

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A researcher wants to compare the performance of students living with their parents and

the performance of these students whose parents are working. Random samples were

taken from two normally distributed groups of population. 25 students who are living

with their parents posted an average grade of 91.27  with standard deviation of 3,

whereas the 20 randomly selected students whose parents are working abroad have an

average grade of 88.72 with standard deviation of 3.4. Test whether there is a significant

difference between the two groups of students at 0.05 level of significance.

State the null and alternative hypotheses.

Identify if it is one-tailed test or two-tailed test.

Find its critical value and identify the rejection region.

Compute the pooled variance.

Compute the test statistic.

State the decision and conclusion.

the number of motorcycles sold annually by salespeople is normally distributed with a standard deviation of 15. A random sample of 300 salesperson taken and the mean number of motorcycles sold annually was found to be 75. find the 99% confidence interval estimate of the population mean

Question 4 [25]

The amount of time devoted to preparing for a statistics examination by students is a normally

distributed random variable with a mean of 17 hours and a standard deviation of 5 hours.

Required:

a) What is the amount of time below which only 15% of all students spend studying?

b) What is the amount of time above which only one third of all students spend studying?

c) What is the probability that a student spends between 16 and 20 hours studying?

d) What is the probability that a student spends at least 15 hours studying?

e) What is the probability that a student spends at most 18 hours studying?

Question 3 [25]

Suppose that a mobile telecommunication company’s helpline receives five calls, on average, per

minute.

Required:

a) Discuss the difference between the Binomial probability distribution and the Poisson

probability distribution.

b) How many calls does the company expect to receive in a period of 30 minutes?

c) What is the probability that the company will receive at most four calls in a period of 4

minutes?

d) What is the probability that the company will receive at least three calls in a period of 5

minutes?

e) What is the probability that the company will receive between six and nine calls in a period

of 2 minutes?

Direction: Answer the given problem.

The Guidance Counselor of your school claims that the Grade 11 students spend an average of 11.28 hours in a week doing performance tasks with standard deviation of 1.64. Your adviser thinks that students spend more time in doing performance tasks, so he decided to conduct his own research. He used a sample of 46 Grade 11 students and obtained a mean of 11.83. Is there enough evidence at 0.05 level of significance that the students spend 11.28 hours in a week doing performance tasks?

Sketch a normal curve that has a mean of 60 and a standard deviation of 12. On the same x-axis, sketch another normal curve that has a mean of 90 and a standard deviation of 6. Describe the two normal curves.

Random samples of size 3 are taken from a population of the numbers 3, 4, 5, 6, 7, 8, and 9.

1. How many samples are possible? 

2. Construct the sampling distribution of the sample means.