In Chad's reading class, all the students are reading the same book. The school bought each student a book at $7 per book. If th
2 answers:
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Answer:
Yes, since the test statistic value is greater than the critical value.
Step-by-step explanation:
Data given and notation
represent the mean for the downtown restaurant
represent the mean for the freeway restaurant
represent the sample standard deviation for downtown
represent the sample standard deviation for the freeway
sample size for the downtown restaurant
sample size for the freeway restaurant
t would represent the statistic (variable of interest)
significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the true mean of revenue for downtown is higher than for freeway restaurant, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, 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 whether the means of two groups are equal to each other.
Determine the critical value.
Based on the significance level and
we can find the critical values from the t distribution dith degrees of freedom df=36+36-2=55+88-2=70, we are looking for values that accumulates 0.025 of the area on the right tail on the t distribution.
For this case the value is
Calculate the value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
What is the p-value for this hypothesis test?
Since is a right tailed test the p value would be:
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given we see that
so we can conclude that we reject the null hypothesis, and the true mean for the downtown revenue restaurant seems higher than the true mean revenue for the freeway restaurant.
The best option would be:
Yes, since the test statistic value is greater than the critical value.
Answer:
θ = -33.69°
Step-by-step explanation:
For Φ>0 and Φ<0 (in general Φ≠nπ where n is an integer), sin(Φ) ≠ 0
Dividing both equations:
Therefore:
arctan(θ) = -2/3
θ = -33.69°
The answer does not depend on the sign of Φ, in fact we just need that the sine does not become zero, which occurs when Φ is equal to an integer times π (radians) or 180 (degrees)
Have a nice day!
Answer:
.
Step-by-step explanation:
The linear approximation is given by the equation
Linear approximation is a good way to approximate values of as long as you stay close to the point
, but the farther you get from
, the worse your approximation.
We know that,
Next, we need to plug in the known values and calculate the value of :
Then
.