The mean annual tuition and fees for a sample of 15 private colleges was $41,200 with a standard deviation of $5,300. A dotplot shows that it is reasonable to assume that the population is Approximately normal. You wish to test whether the mean tuition and fees for private colleges is Different from $38,000.
State the null and alternate hypotheses.
A) $H _ { 0 } : \mu \neq 38,000 , H _ { 1 } : \mu = 38,000$
B) $H _ { 0 } : \mu = 41,200 , H _ { 1 } : \mu \neq 41,200$
C) $H _ { 0 } : \mu = 38,000 , H _ { 1 } : \mu = 41,200$
D) $H _ { 0 } : \mu = 38,000 , H _ { 1 } : \mu \neq 38,000$

Question

The mean annual tuition and fees for a sample of 15 private colleges was $41,200 with a standard deviation of $5,300. A dotplot shows that it is reasonable to assume that the population is Approximately normal. You wish to test whether the mean tuition and fees for private colleges is Different from $38,000.
State the null and alternate hypotheses. 
A) $H _ { 0 } : \mu \neq 38,000 , H _ { 1 } : \mu = 38,000$
B) $H _ { 0 } : \mu = 41,200 , H _ { 1 } : \mu \neq 41,200$
C) $H _ { 0 } : \mu = 38,000 , H _ { 1 } : \mu = 41,200$
D) $H _ { 0 } : \mu = 38,000 , H _ { 1 } : \mu \neq 38,000$

Quizplus · Accepted Answer

The null hypothesis should always be the statement that we are testing, which in this case is whether the mean tuition and fees for private colleges is different from $38,000. Therefore, the null hypothesis should be stated as H0: μ = 38,000, and the alternative hypothesis should be H1: μ ≠ 38,000, indicating a two-tailed test. Choice D correctly represents these hypotheses.

The Mean Annual Tuition and Fees for a Sample of 15