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Answer:
a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.
b. z=1.24. No, it can not be concluded that the population mean is greater than 50.
c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.
Step-by-step explanation:
We have a hypothesis test for the mean, with the hypothesis:
The sample size is n=55 and the population standard deviation is 6.
The significance level is 0.05.
We can calculate the standard error as:
For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.
a. If the sample mean is M=52.5, the test statistic is:
The null hypothesis is rejected, as z>zc and falls in the rejection region.
b. If the sample mean is M=51, the test statistic is:
The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.
c. If the sample mean is M=51.8, the test statistic is:
The null hypothesis is rejected, as z>zc and falls in the rejection region.
Because this is a right angle triangle, we can use the Pythagorean theorem to find the missing leg.
The Pythagorean theorem is this:
The Pythagorean theorem tells us if you square both the legs then add them up together, you will get the length of the hypotenuse squared.
We know one leg is 24 and the hypotenuse is 26. Plug them into the equation.
24^2 + b^2 = 26^2
Solve for b.
24^2 + b^2 = 26^2
576 + b^2 = 26^2
576 + b^2 = 676
b^2 = 100
Take the square root of both sides.
b = 10
So, the other leg of the triangle is 10 units long.
The Pythagorean theorem is this:
The Pythagorean theorem tells us if you square both the legs then add them up together, you will get the length of the hypotenuse squared.
We know one leg is 24 and the hypotenuse is 26. Plug them into the equation.
24^2 + b^2 = 26^2
Solve for b.
24^2 + b^2 = 26^2
576 + b^2 = 26^2
576 + b^2 = 676
b^2 = 100
Take the square root of both sides.
b = 10
So, the other leg of the triangle is 10 units long.