Statistics and Probability Answers

Exercise 30 examined the association between the duration of a roller coaster ride and the height of its initial drop, reporting that R^2= 15.2%
write a sentence summarizing what the R^2 says about this regression

the mitch hawker poll ranked the top 10 steel roller coasters in 2011. a regression to predict duration from drop has R^2 = 15.2%
a) what are the variables and units in this regression
b) what units does the slope have
c) do you think the slope is positive or negative? explain

A lawsuit has been brought by female managers of a company. Recently the company decided to promote three of eight mid-level managers to top vice-president positions. Of the eight mid-level managers, five were women and three were men, yet all of the promotions went to the men. The lawyer for the women believes that they have a case if the probability of only men getting these three promotions by chance alone is less than 5%. Do the female employees have a case? Justify your answer.

The following table gives for a sample of married women, the level of education
and marriage adjustment score:
Marriage Adjustment Score

Low High Very High
Middle School 25 5 10
Level of High School 50 30 40
Education College 120 60 60

Can you conclude from the above, the higher the level of education, the greater is
the degree of adjustment in marriage? Justify.

In a partially destroyed laboratory, record of an analysis of correlation of data,
only the following results are legible:
Variance of X = 9
Regression equations are
(i) 8x −10y + 66 = 0
(ii) 40x −18y − 214 = 0
Find out the following missing results.
(i) The means of X and Y
(ii) The coefficient of correlation between x and y
(iii) The standard deviation of Y

A company is manufacturing cotton threads under different speeds of spindle. The
tensile strength of the thread is a parameter that is of interest to the customer. Data
on different speeds of spindle and corresponding tensile strength on 5 samples is
given. Perform ANOVA to find out which is the most suitable speed for the
spindle so as to have maximum tensile strength.

Speed Tensile strength
1 2 3 4 5
10 22.2 20.6 21.5 20.6 22.0
20 24.2 25.0 24.8 20.7 21.0
30 25.0 23.2 21.7 22.5 20.9

The following data were obtained from two random samples. Test whether the
samples come from the same normal population at 5% level of significance.
No. Size Mean Sum of squares of deviation
from mean
1 10 15 90
2 12 14 108

The following table gives the yield of a hybrid variety of wheat, in quintals per
acre from 17 trial plots of land treated with four types of fertilizers
Treatment with fertilizer
A B C D
24 31 39 38
39 25 41 32
35 26 33 35
21 40 34
45 26
Estimate the number of orchards in the district.

The chances that a visit to a primary health centre (PHC) results in neither lab
work, nor referred to a specialist is 35%. Out of those coming to a PHC, 30% are
referred to a specialist, and 40% require lab work. Find the probability that a visit
to a PHC results in both lab work and referral to a specialist.

Consider a random sample (WOR) of two households from a population of
households having monthly income (in $) as follows:
Household 1 2 3 4 5
Income 1000 1200 900 1500 1300
Enumerate all possible samples (WOR) of size 2 and show that the sample mean
gives an unbiased estimate of population mean.