Sandy is designing a circular garden as shown in this image. Her plan is to fill the rectangular region with hyacinths. She will
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Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense
Step-by-step explanation:
Data given and notation
The mean and sample deviation can be calculated from the following formulas:
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is lower than 30 or no, the system of hypothesis are :
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
We need to calculate the degrees of freedom first given by:
Since is a one-side left tailed test the p value would given by:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense
Answer:
s = 16.97 units
Step-by-step explanation:
Since this is a right triangle, we can use trigonometry to figure out the lengths of the sides.
Look at the 45 degree angle. We can use the opposite side (12) and the hypotenuse (s) to solve for s.
Opposite and hypotenuse is sine, so we are using sine. The sine of 45 degrees is 0.70710678118. Make an equation like so:
- 0.70710678118 =
, and we are solving for s.
Put a 1 in the denominator of sine(45 degrees) so you can cross-multiply.
Cross multiply.
- 0.70710678118s = 12
Divide both sides by sine(45 degrees).
- s = 16.97
The length of side s is 16.97 units.
Another way to have done this problem is to use the Pythagorean theorem: a^2 + b^2 = c^2
Substitute 12 for a and b and solve for c, the hypotenuse.
- (12)^2 + (12)^2 = c^2
Evaluate the exponents.
- 144 + 144 = c^2
Add them together.
- 288 = c^2
Square root 288 to solve for c.
c = 16.97, which is the same answer as you got using trigonometry.