The perimeter of a rectangle is 37. The length is 1 less than 12 times the width. What is the length and width of the rectangle
1 answer:
You might be interested in
Answer:
a-1) Reject H0 if zcalc > 1.645
a-2)
a-3) ii. False
b) ii. No
c) iii. n π > 10 and n(1 − π ) > 10
Step-by-step explanation:
1) Data given and notation
n=114 represent the random sample taken
X=36 represent the people that were issued to a single-earner family or individual
estimated proportion of people that were issued to a single-earner family or individual
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
(a-1) H0: π ≤ .28 versus H1: π > .28. Choose the right option. Reject H0 if zcalc > 1.645 Reject H0 if zcalc < 1.645 a b
We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.28.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
The rejection zone would be on this case :
Reject H0 if zcalc > 1.645
Since is a right tailed test
(a-2) Calculate the test statistic. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.) Test statistic
Since we have all the info requires we can replace in formula (1) like this:
(a-3) The null hypothesis should be rejected.
False, since our calculated value is less than our critical value we Fails to reject the null hypothesis
(b) Is this a close decision?
False the calculated value is significantly less than the critical value so we FAIL to reject the null hypothesis with enough confidence.
(c) State any assumptions that are required.
In order to satisfy the conditions we need the following two requirements:
iii. n π > 10 and n(1 − π ) > 10
And are satisfied:
114*0.28=31.92>10
114(1-0.28)=82,08>10
Answer:
Tina would save the same amount using either option after 20 months.
With either option, Tina would save $700.
Step-by-step explanation:
This problem can be modeled by a first order equation:
Where Tina's saved money after n months is:
S(n) = S(0) + rn, where S(0) is the money put away initially and r is how much she saves every month.
The first option is to put $500 away initially and save $10 every month, so:
The second option is to put $100 away initially and save $30 every month, so:
After how many months would Tina save the same amount using either option?
It will happen at the month n in which , so:
500 + 10n = 100 + 30n
500 - 100 = 30 - 10n
400 = 20n
20n = 400
n = 20.
Tina would save the same amount using either option after 20 months.
How much would she save with either option?
We can choose or
, since they are equal
With either option, Tina would save $700.