11c - 2d = -2 c + 8d = 8 using the substitution method
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The probability that a student participates in both sports and drama is .
If and
are any two events, then the probability of the joint event
is given by the following formula:
Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.
Suppose denotes that "a student participates in sports" and
denotes that "a student participates in drama".
So, we have ,
,
.
We want to find the probability that a student participates in both sports and drama i.e., we want to find .
By the above formula, we obtain:
Therefore, the probability that a student participates in both sports and drama is .
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We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.
Given,
The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.
In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.
To report the large-sample z statistic and its p-value,
Null hypothesis,
H₀ : p = 0.79
Alternative hypothesis,
Ha : p < 0.79
Level of significance, α = 0.01
Under H₀
Test statistic,
Z₀ = -7.948
The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by
P-value = P(z <-7.945)
= 0.000 (from z-table)
Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.
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