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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- IV EXAMINATION WINTER 2018
Subject Code:3640001 Date:16/11/2018
Subject Name: Basic Statistics
Time:10.30 am to 1.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Explain different level of data measurement with examples?
07

For each class interval of the frequency distribution given, determine the class midpoint the relative frequency and the cumulative frequency
Class interval
Frequency
20 -25
8
25 -30
6
30-35
5
35-40
12
40-45
15
45-50
7
07
Q.2

A data set contains the following eight values
4 3 0 5 2 9 4 5.
Find the range.
Find the mean absolute deviation.
Find the sample variance.
Find the sample standard deviation.
Find the interquartile range.
07

Following data represent the cost of sample of 30 postal mailing by a company
3.67
2.75
9.15
5.11
3.32
2.09
1.83
10.94
1.93
3.89
7.20
2.78
6.72
7.80
5.47
4.15
3.55
3.53
3.34
4.95
5.42
8.64
4.84
4.10
5.10
6.45
4.65
1.97
2.84
3.21
Using dollars as a stem and cents as a leaf, construct a stem and leaf plot of the data.
07
OR

According to the U.S . Bureau of Labor Statistics, 75% of the women 25 through 49 years of age participate in the labor force. Suppose 78% of the women in that age group are married. Suppose also that 61% of women 25 through 49 years of age are married and are participating in the labor force.
a. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force?
b. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force but not both?
c. What is the probability that a randomly selected woman in that age group is neither married nor participating in the labor force
07
Q.3

Machines B and C all produce the same two parts X and Y of all the parts produced Machine A Produces 60% Machine B produces 30% and Machine C produces 10% . In addition
07
2
40% of the parts made by machine A are part X.
50% of the parts made by machine B are part X.
70% of the parts made by machine C are part X.
A part produced by this company is randomly sampled and is determined to be an X part. With the knowledge that it is an X part revise the probabilities that the part came from machine B or C.

Explain different sampling Methods
07
OR
Q.3

W.Edwards Deming in his red bead experiment had a box of 4000 beads, of which 800 were red and 3200 were white .Suppose a researcher were to conduct a modified version of the red bead experiment. In her experiment, she has a bag of 20 beads, of which 4 are red and 16 are white .This experiment requires a participant to reach into the bag and randomly select five beads without replacement.
a. What is the probability that the participant will select exactly four white beads?
b. What is the probability that the participant will select exactly four red beads?
c. What is the probability that the participant will select all red beads?
07

Suppose you are working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. Determine the value of x from the following information.
a. Sixty percent of the values are greater than x.
b. x is less than 17% of the value.
c. Twenty two percent of the values are less than x.
d. X is greater than 55% of the values.
07
Q.4

Suppose a subdivision on the southwest side of Denver Colorado contains 1500 houses. The subdivision was built in 1983. A sample of 100 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $177,000 with a standard deviation of $8,500 what is the probability that the sample average is greater than $185,000?
07

A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4. What is the point estimate of ?.Construct a 94% confidence interval for
07
OR
Q.4

According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays; Suppose 200 executives are randomly surveyed.
a. What is the probability that fewer than 90 of the executives believe employees are most productive on Tuesdays?
b. What is the probability that more than 100 of the executives believe employees are most productive on Tuesdays?
c. What is the probability that more than 80 of the executives believe employees are most productive on Tuesdays?
07

Suppose you want to estimate the average age of all Boeing 737-300 airplanes now in active domestic. U.S service. You want to be 95% confident, and you want your estimate to be within one year of the actual figure. The 737-300 was first placed in service about 24 years ago, but you believe that no active 737-300s in the US domestic fleet are more than 20 years old. How large of a sample should you take?
07
Q.5

A random sample of size 20 is taken resulting in a sample mean of 16.45 and a sample standard deviation of 3.59. Assume x is normally distributed and use this information and to test the following hypothesis.
Ho =16 Ha 16
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3

Compute the sum of squares of error and the standard error of the estimate data, in which regression model was developed to predict the number of FTes at a hospital by number of beds.
X
23
29
29
35
42
46
50
54
64
66
76
78
Y
69
95
102
118
126
125
138
178
156
184
176
225
07
OR
Q.5

List properties of Point Estimator. Explain any one in detail
07

A small business has 37 employees. Because of the uncertain demand for its product the company usually pays overtime on any given week. The company assumed that about 50 total hours of overtime per week is required and that the variance is about 25. Company officials want to know whether the variance of overtime hours has changed. Given here is a sample of 16 weeks of overtime data (in hours per week). Assume hours of overtime are normally distributed .Use these data to test the null hypothesis that the variance of overtime data is 25. Let
57
56
52
44
46
53
44
44
48
51
55
48
63
53
51
50
07