Statistics and Probability Answers

the officers of science club are planning to sell 125 tickets to be raffled during the school's foundation day. One ticket will win Php2,000 and the other tickets will win nothing. If you will buy one ticket, what will be your expected gain E(X)?

The processors of Peanut's Butter indicate on the label that the bottle contains 16 ounces of peanuts. The standard deviation of the process is 0.5 ounces. A sample of 36 bottles from the last hour's production revealed a mean weight of 16.12 ounces per bottles, at the α = 0.05 is the process out of control? That is, can we conclude that the mean amount per bottle is different from 16 ounces. Find the critical value?

Question 1 (a). In each of the following research situations, state the type of statistical test that may be used to answer the research question. Give a brief reason for your answer.

 (ii). “As far as intelligence is concerned, women do not differ from the general population”. This is a claim by some researchers on gender issues. To test this claim, 100 women were sampled from the general population and their intelligence (IQ) measured. It was found that the mean IQ of the female sample was equal to 110. Assuming that the mean IQ in the general population is equal to 105 with a standard deviation of 10, how true is the claim by the researchers?

MATH205

Question 1 (a). In each of the following research situations, state the type of statistical test that may be used to answer the research question. Give a brief reason for your answer.

(i). The mean age of all 2000 students enrolled in the KCC weekend programme since the programme was started is equal to 35 years. The mean age of the 500 students who were enrolled in the programme during the 2020/2021 academic year is 40 years with standard deviation of 8 years. Is true that the 500 students enrolled in the programme during the 2020/2021 academic year are older than the population of all students enrolled in the programme?

As a Senior High School Student how much time do you spent in studying

and answering the activities in your modules? Do you

spend 25 hours in a week er

more than that? Suppose that the average number of hours spent by senior high

tool students in your school for their modular classes in a week is 25 hours with

4 standard deviation of 4 hours. Assuming that the study is true and the data is

Normally distributed. What is the probability that a random sample of 12 senior

high school students spends more than 24 hours?

(b) (i) A random variable 'X' has the density function:

f(x) = K. — in- < x <

Random samples of size n=2 are drawn from a finite population consisting of the numbers 5,67,8 and 9. Compute the mean, variance and standard deviation of the population, and the me a variance and standard deviation of the sample means. Showtablr with complete solutions

QUESTION 1

A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A

researcher randomly selects 20 women and obtained these data

3 | 2 | 1

3 | 7 | 2

9 | 4 | 6

6 | 8 | 0

5 | 6 | 4

2 | 1 | 3

4 | 1

At α=0.05 can it be concluded that the average is still 5.8 visits per year? Use P-value method.

a) State the hypothesis and identify the claim.

b) State the value of d.f.

c) Compute the test value.

d) Find the P-value.

e) Make the decision

f) Summarize the results

Number of students, mean and standard deviation of std X students of three different schools are as follows -

Govt Boys High School: N = 60, Mean = 38, SD = 5.2

Govt Girls High School: N = 50, Mean = 42, SD = 4.8

Govt Coeducation High School: N = 80, Mean = 46, SD = 6.1

I. Find how many students of Govt Boys High School are above the mean of Govt Girls High School

II. Find how many students of Govt Boys High School are above the mean of Govt Coeducation High School.

III. Find how many students of Govt Girls High School are above the mean of Govt Coeducation High School

IV. Find how many students of Govt Coeducation High School are below the mean of Govt Boys High School 

Observe yourself in a day. Find out how many hours you spend in the following

activities: house chores, answering Self Learning Modules, planting/gardening,

using social media like Facebook, messenger, tiktok, Instagram, and YouTube,

listening to music, watching television, and sleeping. Record your data. Construct a

probability distribution, then compute the mean (u), variance (02), and standard

deviation (o) of the probability distribution that you made.