A local real estate agent claims that the median selling price of homes in a major midwestern city is more than $200,000.Suppose a random sample of 100 homes sold in the last six months is taken and 53 sold for over $200,000.Using ? = .01,test the real estate agent's claim.What do you conclude about the selling prices of the homes?
A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
$$z = \frac { ( 53 + .5 ) - \left( .5 ^ { * } 100 \right) } { .5 * \sqrt { 100 } } = \frac { 3.5 } { 5 } = .70$$

Question

Quizplus · Accepted Answer

We need to conduct a one-tailed hypothesis test with a significance level of 0.01.

Null hypothesis: The median selling price of homes is less than or equal to $200,000.
Alternative hypothesis: The median selling price of homes is greater than $200,000.

Since the sample size is large (n = 100) and we are dealing with median values, we cannot assume a normal distribution. Instead, we use the sign test. The test statistic is the number of observations in the sample that are greater than $200,000.

Under the null hypothesis, we expect exactly 50 of the observations to be greater than $200,000. We calculate the p-value as the probability of getting 53 or more observations greater than $200,000 under the null hypothesis.

Using a binomial distribution, we find the p-value to be 0.0668. Since this is greater than the significance level of 0.01, we fail to reject the null hypothesis. We do not have enough evidence to conclude that the median selling price of homes is greater than $200,000.

A Local Real Estate Agent Claims That the Median Selling z=(53+.5)−(.5∗100).5∗100=3.55=.70z = \frac { ( 53 + .5 ) - \left( .5 ^ { * } 100 \right) } { .5 * \sqrt { 100 } } = \frac { 3.5 } { 5 } = .70z=.5∗100​(53+.5)−(.5∗100)​=53.5​=.70

A Local Real Estate Agent Claims That the Median Selling $z = \frac { ( 53 + .5 ) - \left( .5 ^ { * } 100 \right) } { .5 * \sqrt { 100 } } = \frac { 3.5 } { 5 } = .70$