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2. The population mean length of a chocolate wafer stick is 86 mm long with a standard deviation of 6 mm. A sample of 20 sticks are taken. What is the probability that
a. the sample mean is not less than 84 mm?
b. the sample mean is not more than 87 mm?
c. the sample mean differs from the population mean by at most 4 mm?
A married couple, purchased their home in December 1989 for R289 000. The house was appraised in January 2008for R927 00. What was the annual rate of appreciation on the home during this period ?
2) For a certain type of fluorescent light in a large building, the cost per bulb of replacing bulbs all at once is much less than if they are replaced individually as they burn out. It is known that the lifetime of these bulbs is normally distributed, and that 60% last longer than 2500 hours, while 30% last longer than 3000 hours.
a) What are the approximate mean and standard deviation of the lifetimes of the bulbs?
b) If the light bulbs are completely replaced when more than 20% have burned out, what is the time between complete replacements?
We want to know if 2 different professors are teaching two different section of the same
statistics course differently. The following are the test scores for the 15 students from
section (A) and 15 students from section (B).
Section (A) 81 83 72 74 79 95 62 90 86 72 67 79 93 80 75
Section (B) 79 82 75 82 81 97 64 88 80 74 63 79 94 85 68
Use the sign test at 0.05 level of significance
The nutritionist and medical doctors have always believed that Vitamin C is highly
effective in reducing the incidents of colds. To test this belief, a random sample of 13
persons is selected and they are given daily doses of Vitamin C under medical supervision
over a one-year period. The number of codes each person catches during the year is
recorded and a comparison is made with the number of colds contracted by each such
person during the previous year. This comparison is tabulated as follows, along with the
sign of the change.
Observation 1 2 3 4 5 6 7 8 9 10 11 12 13
Without
Vitamin C
7 5 2 3 8 2 4 4 3 7 6 2 10
With
Vitamin C
2 1 0 1 3 2 3 5 1 4 4 3 4
Use the sign test at 0.05 level of significance, determine if Vitamin C is effective in reducing
colds.
The personnel director of a company wishes to select applicants for advanced training
without regard to sex. Let ‘W’ denote women and ‘M’ denote men and the pattern of arrival
be ‘M WWW MMM WW M WWWW MMMM W M W MM WWW MM W MMMM
WW M WW MMMM WW M WWWW MM WW M W M WW’. Will you conclude that
the applicants have arrived in a random fashion?
29) The following arrangement shows the rise(U) or fall(D) in the price of an equity share on
40 consecutive trading days on which its price did not remain the same:
U U D D U U U D U U U D D U D D D U D D U D D U U U U D D D D U U D U U D D D
U
Test the hypothesis that this arrangement of Us and Ds is random at α =0.05 level of
significance.
30) The sequence of occurrence of ‘zeros’ and ‘ones’ in a message sent in a digital code is
shown below. Test at 5 percent whether the sequence of ‘0’ and ‘1’ is random 00110 11011
00001 11100 00110 11001 11110 00011 00100 11000 11100 00011 11100 00000 11111
10001 11000 10001 01110.
Vanaspati oil is marketed in tins of 10 kg. A sample of 20 tins showed the mean weight as
9.5kg with standard deviation of 3 kg. Does the sample justify the claim that the mean
weight is 10 kg. Mention the level of significance, you use.
24) A random sample of 16 observations has mean 103.75cm. The sum of the squares of the
deviations from the mean is 843.75 cm. Can this sample be regarded as coming from the
population having 108.75cm as the mean?
25) A company supplies tooth-paste in a packing of 100gm. A sample of 10 packing’s gave the
following weights in gm.
100.5, 100.3, 100.1, 99.8, 99.7, 99.7, 100.3, 100.4, 99.2, 99.3
Does the sample support the claim of the company that the packing weighs 100 gm?
The manufacturer of a patent medicine claimed that it is effective in relieving 90% of the
people suffering from the disease. From a sample of 200 people using the medicine 160
were relived of suffering. Determine if the claim is legitimate.
21) In 324 throws of a six face die odd points appeared 181 times. Would you say that the die
is ‘fair’? State the level of significance, you use.
22) In a random sample of 400 persons taken from a large population 120 were females. Can
it be said that male and females are in the ration 5:3 in the population. Use 1% level of
significance.
The mean breaking strength of cables supplied by a manufacturer is 1800 with standard
deviation 100. By a new technique in the manufacturing process, it is claimed that the
breaking strength of the cable has increased. In order to test the claim a sample of 50 cables
is tested. It is found that the mean breaking strength is 1850. Can we support the claim at
1% level of significance?
19) A coin is tossed 400 times and was found to result in head 245 times. Can we conclude the
coin is fair?
A machine is claimed to produce nails of mean length 5cm. and standard deviation of
0.45cm. A random sample of 100 nails gave 5.1cm. as their average length. Does the
performance of the machine justify the claim? Mention the level of significance you apply?
16) The mean height of random sample of 100 individuals from a population is 160 cms. The
S.D. of the sample is 10cms. Would it be reasonable to suppose that the mean height of the
population is 165cms?
17) A sample of 50 pieces of certain type of string was tested. The mean breaking strength
turned out to be 14.5 gms. Test whether the sample is from a batch of a string having a
mean breaking strength of 15.6 gms and standard deviation of 2.2 gms.
