Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims th
1 answer:
Answer:
0.9256
Step-by-step explanation:
Given that a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit
Let X be the number of customers who buy from her store, on a certain day of the week, buy coffee during their visit
X is Binomial (35, 0.55)
since each customer is independent of the other and there are two outcomes.
By approximation to normal we find that both np and nq are >5.
So X can be approximated to normal with mean = np = 19.25
and std dev =
Required probability = prob that fewer than 24 customers in the sample buy coffee during their visit on that certain day of the week
= (after effecting continuity correction)
= 0.9256
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Answer:
(1) The degrees of freedom for unequal variance test is (14, 11).
(2) The decision rule for the 0.01 significance level is;
- If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.
- If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.
(3) The value of the test statistic is 0.3796.
Step-by-step explanation:
We are given that you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne's attire with those of Calvin Klein.
The following is the amount ($000) earned per month by a sample of 15 Claiborne models;
$3.5, $5.1, $5.2, $3.6, $5.0, $3.4, $5.3, $6.5, $4.8, $6.3, $5.8, $4.5, $6.3, $4.9, $4.2 .
The following is the amount ($000) earned by a sample of 12 Klein models;
$4.1, $2.5, $1.2, $3.5, $5.1, $2.3, $6.1, $1.2, $1.5, $1.3, $1.8, $2.1.
(1) As we know that for the unequal variance test, we use F-test. The degrees of freedom for the F-test is given by;
Here, = sample of 15 Claiborne models
= sample of 12 Klein models
So, the degrees of freedom = () = (15 - 1, 12 - 1) = (14, 11)
(2) The decision rule for 0.01 significance level is given by;
- If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.
- If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.
(3) The test statistics that will be used here is F-test which is given by;
T.S. = ~
where, = sample variance of the Claiborne models data =
= 1.007
= sample variance of the Klein models data =
= 2.653
So, the test statistics = ~
= 0.3796
Hence, the value of the test statistic is 0.3796.
We can use the law of cosines as follows:
We can rewrite this equation as