CHAPTER 2 TESTING OF HYPOTHESIS
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Question for Practice (Important Question)
(Testing of Hypothesis)
1. Write short notes on
(a) Hypothesis and its type.
(b) Steps used in Testing of Hypothesis.
(c) Tails of test in testing of Hypothesis.
2. A random sample of 100 pen drives selected from a batch of 2000 pen drives shows that the average
thickness of the pen drive is 0.35 with a standard deviation 0.048. Doan the samples from the lot have
average thickness of 0.34? [0.85]
3. A dealer of a DELL company located at New Road claimed that the average lifetime of a multimedia
projector produced by Dell Company is greater than 60,000 hours with a standard deviation of 6000 hours.
In order to test his claim, a sample of 100 DELL projectors was taken and the average lifetime was
monitored and it was found to be 55,000 hours. Test the claim of the dealer at 5% level of significance.
4.A study claims that all the adults spend an average of 14 hours or more on chores during a weekend. A
researcher wanted to check this claim is true. A random sample of 200 adults taken by this researcher
showed that these adults spend an average of 13.75 hours on chores during a weekend with standard
deviation of 3 hours. Test the claim is true at 5% level of significance. [1.48]
5. A random sample of size 35 taken from a normal population with standard deviation 5.2 has a mean
81.A second sample of size 36 taken from other normal population with a standard deviation 3.4 has a
mean 76. Test whether the two samples mean do not differ significantly at 5% level of significance. [4.78]
6. A company claims that its light bulbs are superior to those of the competitor on the basis of study
which showed that a sample of 40 of its bulbs had an average life time 628 hours of continuous use with
a standard deviation of 27 hours. While sample of 30 bulbs made by the competitor had an average life
time 619 hours of continuous use with a standard deviation of 25 hours. Test at 5% level of significance,
whether this claim is justified.
7. In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled out into a
wrong line. Test the hypothesis that actually 30% of all drivers make this mistake at the given
intersection at α=0.05 using p value. [p value=0.0166]
8.To check on an ambulance services claim that at least 40% of its calls are life tereatening emergencies,
a random sample was taken from its files and it was found that only 49 out of 150 calls were life
threatening emergencies. Test the claim at 1% level of significance. [p=0.033 ]
9. In location 1, there are 250 corona positive cases out of 460 persons and in location 2, 250 positive
cases reported out of 650 persons. Can it be concluded that the proportion of corona positive cases is
higher in location 1 compared to location 2? Test at 10% level of significance.
10.A machine puts out 16 imperfect articles in a sample of 500. After the machine is overhauled, it puts
3 imperfect articles in a batch of 100. Has the machine improved? [z=0.105]
11. Ten patients are selected at random from a population of patients and their blood pressure recorded
are as follows: 125,147,118,145,140,128,155,150,160,149. Do the data support the hypothesis that the
population average blood pressure of patients is 135? Use 5% level of significance. [t=1.53]
12.Sample of two types of electric bulbs were tested for length of life and following results were
obtained.
Brand A BrandB
Sample Size 15 12
Mean 1250 hours 1100 hours
standard deviation 30 hours 40 hours
Test whether the electronic bulbs of brand A is superior to the electronic bulbs of brand B.[t=10.71]
13.Ten students were given intensive training on python for a month. the scores obtained in tests I to
test V given below.
S.N. of students 1 2 3 4 5 6 7 8 9 10
Marks in 1st test 50 52 53 60 65 67 48 69 72 80
Marks in 5th test 65 55 65 65 60 67 49 82 74 86
Does the score from test I to test V show an improvement ? Test at 5% level of significance. [t=-2.57]
14. A company , developing animal fodder that enhances weights is conducting research on two types of
fodders A and B. Two groups of animals, one consisting 12 animals were feed on fodder A and other
group consisting 10 animals on B for a period of 4 months. the record of weight gaines in kilograms after
the
Group 1 25 32 30 24 24 20 30 23 28 32 33 25
Group 2 44 34 22 17 45 40 41 30 32 35
Test if two fodders differ significantly to enhance the weight 5% level of significance. [t=-1.998]