Statistics Assignment 2

Assignment NO. 2 week9-week14
Student Full Name:___________________________________ .
Student ID:__________________________________________ .
CRN No:____________________________________________ .
STATISTICS
(STAT-101)
Pre-MBA
Due Date: April 06, 2019
Total Marks: 7
Branch: _____________________________________________.

STATISTICS (STAT-101) Pre MBA
Attempt all the Questions (1 mark each):
1. A research conducted by the University of Michigan claimed that there are more
female drivers in the USA than male drivers. A researcher decides to test this claim on
his state. In his simple random sample of 900 observations, he noticed that 468 of 900
were women. At  = 0.05, is there enough evidence to support the claim?
(Use the P-value method where P ( z<1.20 )=0.8849)
Answer
We sought to test the following hypothesis;
Null hypothesis (H0): There is no significant difference in the proportion of female
and male drivers in the USA.
Alternative hypothesis (HA): There is significant difference in the proportion of
female and male drivers in the USA.
The p-value is given as 0.8849 (a value greater than 5% level of significance), we
therefore fail to reject the null hypothesis and conclude that there is no significant
difference in the proportion of female and male drivers in the USA. There is no
enough evidence to support the claim by the researcher.
2. A sample of 100 body temperatures has a mean of 98.8 °F. Assume that σ is known to
be 0.6°F. Use a 0.05 significance level to test the claim that the mean body
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temperature of the population is equal to 98.6°F, as is commonly believed. Is there
sufficient evidence to conclude that the common belief is wrong?
(Use the P-value method where P ( z<3.33 ) =0.9996)
Answer
We seek to test the following hypothesis;
H0 : μ=98.6
H A : μ<98.6
Z= x−μ
σ / √n = 98.8−98.6
0.6 / √100 = 0.2
0.06 =3.3333
P ( z<3.33 )=0.9996)
The p-value is 0.9996 (a value greater than 5% level), we therefore fail to reject the
null hypothesis and conclude that the common belief is correct.
3. A simple random sample of 25 filtered 100 mm cigarettes is obtained and the tar
content of each cigarette is measured. The sample has a mean of 15 mg and a standard
deviation of 4 mg. Use a 0.05 significance level to test the claim that the mean tar
content of filtered 100 mm cigarettes is less than 20 mg, which is the mean for
unfiltered king size cigarettes. What do the results suggest about the effectiveness of
the filters?
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