A researcher claims that the average annual salary of part-time community college instructors is at least $45,000. To test this claim, a sample of 25 part-time community college instructors is selected at random. The sample average is $42,500 with a sample standard deviation of $3,100. State the null and alternative hypotheses for used to test this claim.

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Step-by-step explanation:

Solution:-

- The researcher claims :

" the average annual salary of part-time community college instructors is at least $45,000 "

- We will extract the claim made by the researcher to be the Null hypothesis:

                     Null Hypothesis : μ ≥ $45,000

- Any statement otherwise, or point of rejection criteria will denote the Alternate hypothesis that disbands the claim that:

" the average annual salary of part-time community college instructors is less than $45,000 " :

                    Alternate Hypothesis : μ < $45,000

- This type of test with a sample size of n = 25 < 30 and population standard deviation is also not given hints the use t-test statistics and t-critical value reject the claim.

                     Lower tail - one sample - T-test.

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation: