(a) Determine the null and alternative hypotheses, (b) explain what it would mea
ID: 3262743 • Letter: #
Question
(a) Determine the null and alternative hypotheses, (b) explain what it would mean to make a type I error, and (c) explain what it would mean to make a type II error.
Three years ago, the mean price of a single-family home was
$243 comma 770243,770.
A real estate broker believes that the mean price has
increasedincreased
since then.
(a) Which of the following is the hypothesis test to be conducted?
A.
Upper H 0H0:
muequals=$243 comma 770243,770;
Upper H 1H1:
mugreater than>$243 comma 770243,770
B.
Upper H 0H0:
muequals=$243 comma 770243,770;
Upper H 1H1:
munot equals$243 comma 770243,770
C.
Upper H 0H0:
muequals=$243 comma 770243,770;
Upper H 1H1:
muless than<$243 comma 770243,770
(b) Which of the following is a type I error?
A.
The broker fails to reject the hypothesis that the mean price is
$243 comma 770243,770,
when the true mean price is
greatergreater
than
$243 comma 770.243,770.
B.
The broker rejects the hypothesis that the mean price is
$243 comma 770243,770,
when the true mean price is
greatergreater
than
$243 comma 770.243,770.
C.
The broker rejects the hypothesis that the mean price is
$243 comma 770243,770,
when it is the true mean cost.
(c) Which of the following is a type II error?
A.
The broker fails to reject the hypothesis that the mean price is
$243 comma 770243,770,
when it is the true mean cost.
B.
The broker rejects the hypothesis that the mean price is
$243 comma 770243,770,
when it is the true mean cost.
C.
The broker fails to reject the hypothesis that the mean price is
$243,770 243,770,
when the true mean price is
greatergreater
than
$243,770.
Explanation / Answer
(1) Null HYpothesis : H0 : = $243770
Alternative Hypothesis : Ha : > $243770
(2) Type I error = when null hypothesis is correct but we reject it. That means Mean price of a single-family home has not been increased from $243770 in reality but we reject the null hypothesis. Option C is correct.
(3) Type II error = when null hypothesis is false even we failed to reject it, that means mean price of a single family home is increased from $243770 in reality but we failed to reject the nul hypothesis. Option C is correct.
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