A paper company produces 1,740 notebooks in 2 days. How many notebooks can it produce in 10 days?
1 answer:
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Answer:
Now we can calculate the degrees of freedom for the statistic given by:
And we can calculate the p value given by:
And we can find the p value using the following excel code:
"=1-CHISQ.DIST(19.221,2,TRUE)"
Since the p values is higher than a significance level for example , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.
Step-by-step explanation:
Previous concepts
A chi-square goodness of fit test "determines if a sample data matches a population".
A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".
Solution to the problem
Assume the following dataset:
Size Company/ Heal. Ins. Yes No Total
Small 32 18 50
Medium 68 7 75
Large 89 11 100
_____________________________________
Total 189 36 225
We need to conduct a chi square test in order to check the following hypothesis:
H0: independence between heath insurance coverage and size of the company
H1: NO independence between heath insurance coverage and size of the company
The statistic to check the hypothesis is given by:
The table given represent the observed values, we just need to calculate the expected values with the following formula
And the calculations are given by:
And the expected values are given by:
Size Company/ Heal. Ins. Yes No Total
Small 42 8 50
Medium 63 12 75
Large 84 16 100
_____________________________________
Total 189 36 225
And now we can calculate the statistic:
Now we can calculate the degrees of freedom for the statistic given by:
And we can calculate the p value given by:
And we can find the p value using the following excel code:
"=1-CHISQ.DIST(19.221,2,TRUE)"
Since the p values is higher than a significance level for example , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.
Answer:
a) The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
b) The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
c) The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
d) A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.
Step-by-step explanation:
<em>a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000?</em>
For college graduates in business, the salary distributes normally with mean salary of $53,901 and standard deviation of $15,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
<em>b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000?</em>
<em />
For college graduates in health sciences, the salary distributes normally with mean salary of $51,541 and standard deviation of $11,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
<em>c. What is the probability that a new college graduate in health sciences will earn a starting salary less than $40,000?</em>
To calculate the probability of earning less than $40,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
<em />
<em>d. How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences?</em>
The z-value for the 1% higher salaries (P>0.99) is z=2.3265.
The cut-off salary for this z-value can be calculated as:
A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.