Statistics and Probability Answers

3. Five university students were given an English achievement test before and after receiving instruction in basic grammar. Their scores are shown below:
Student Before After
A 20 18
B 18 22
C 17 15
D 16 17
E 12 9
Should we conclude that future students would show higher scores after instruction? Use the .05 significance level. Use hypothesis testing.

2. Five people who were convicted of speeding were ordered by the court to attend a workshop. A special device placed in their cars kept a record of their speeds for 2 weeks before and after the workshop. The maximum speeds for each person during the 2 weeks before and the 2 weeks after the workshop follow:
Participant Before After
L. B. 65 58
J. K. 62 65
R. C. 60 56
R. T. 70 66
J. M. 68 60
Using the .05 significance level, should we conclude that people are likely to drive more slowly after this workshop? Use hypothesis testing.

1. In a particular country, it is known that college students report falling in love an average of 2.20 times during their college years. A sample of five college students originally from that country but who have spent their entire college career in Canada, were asked how many times they had fallen in love during their college years. Their numbers were 2, 3, 5, 5, and 2.

Using the .05 significance level, do exchange students like these who go to college in Canada fall in love more often than those who complete their studies in their country of origin?

Use the hypothesis–testing steps to answer this.

How do you turn grouped frequency tables into raw data?

After the quizzes are marked, you’re told that the scores on the exam were distributed normally (μ=50, σ=10). You are also told that students with scores in the top 10% will receive a chocolate bar, and students with scores in the top 25% will receive a stick of gum.
a) What is the minimum score needed to receive a chocolate bar?
b)Would a score of 57 earn a stick of gum?

I don't know the steps, so confused!

Of all the smokers in a particular district, 40% prefer brand A and 60% prefer brand B. Of those smokers who prefer brand A, 40% are females, and of those who prefer brand B, 30% are female. What is the probability that a randomly selected smoker prefers brand B, given that the person selected is a female?

Your calculator gives a 95% confidence interval as: (-7.40, 5.80) for the mean difference in dollar value of gifts from family members from your moms side vs your dads side of the family. Explain in regular speaking English (like you're explaining to someone who has never taken statistics) what this interval means if we estimate Mdad-Mmom.

Ten voters were picked at random from those who voted in favour of a certain proposition and twelve from those who voted against it. The following figures give their ages:
In favour 28 33 27 31 29 25 50 30 25 41
Against 31 43 49 32 40 41 48 30 29 39 42 36
At 5% percent level of significance, it is evidence from the data that the mean age of those voting against the proposition is significantly different from the mean of those voting for it?

The height of students in a certain BCOM class is normally distributed with mean and standard deviation .A random sample of 100 students was taken and the 90% confidence interval for was found to be between 175cm and 180cm.
Estimate the :-
(i) value of the sample mean
(ii) value of

A plumber loads his truck each morning with faucets that will be needed for the service calls and other emergency calls that come in that day. Based on past experience, the number of faucets required each day (N) has the following distribution: p(0) =0.05; p(1) = 0.25;
p(2) = 0.5; p(3) = 0.15; p(4) = 0.05.


-Each faucet requires 25 minutes to install. What is the expected number of minutes the plumber will spend each day installing faucets?