Question to test your Steps in Hypothesis Testing knowledge

Question

A community center director claims that the median number of hours volunteers contribute per week is at least $10$ hours. In a random sample of $25$ volunteers, the number of hours they contributed last week (relative to $10$ hours) is:

$15$ volunteers contributed less than $10$ hours
$8$ volunteers contributed more than $10$ hours
$2$ volunteers contributed exactly $10$ hours
i) Identify the claim and state $H sub 0$ and $H_{a}$ .
ii) At the $0.05$ significance level, can you reject the director’s claim? Interpret the decision.

Accepted Answer

i) H0:τ=10H_0:	au=10; Ha:τ10H_{a}:	au ii) Fail to reject H0H_0. At the 5%5\% significance level, there is insufficient evidence to conclude that the true median volunteer hours is less than 1010.

Answer

i)  H0:τ=10H_0:	au=10 ; 10"\u003eHa:τ\u003e10H_{a}:	au\u003e10 ii) Reject H0H_0 . At the 5%5\%  significance level, there is sufficient evidence to conclude that the true median volunteer hours is greater than 1010.

Answer

i) H0:τ=10H_0:	au=10; Ha:τ≠10H_{a}:	au
e10 ii) Reject H0H_0. At the 5%5\% significance level, there is sufficient evidence to conclude that the true median volunteer hours is 1010.

Answer

i) H0:τ=10H_0:	au=10; Ha:τ≠10H_{a}:	au
e10 ii) Fail to reject H0H_0. At the 5%5\% significance level, there is insufficient evidence to conclude that the true median volunteer hours is 1010.

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