Questions: Three years ago, the mean price of an existing single-family home was 243,752. A real estate broker believes that existing home prices in her neighborhood are higher. (a) State the null and alternative hypotheses in words. (b) State the null and alternative hypotheses symbolically. (c) Explain what it would mean to make a Type I error. (d) Explain what it would mean to make a Type II error. (a) State the null hypothesis in words. Choose the correct answer below. A. The mean price of a single family home in the broker's neighborhood is 243,752. B. The mean price of a single family home in the broker's neighborhood is different from 243,752. C. The mean price of a single family home in the broker's neighborhood is greater than 243,752. D. The mean price of a single family home in any neighborhood is 243,752. State the alternative hypothesis in words. Choose the correct answer below. A. The mean price of a single family home in the broker's neighborhood is different from 243,752. B. The mean price of a single family home in the broker's neighborhood is greater than 243,752. C. The mean price of a single family home in the broker's neighborhood is 243,752. D. The mean price of a single family home in any neighborhood is 243,752.

Three years ago, the mean price of an existing single-family home was 243,752. A real estate broker believes that existing home prices in her neighborhood are higher. (a) State the null and alternative hypotheses in words. (b) State the null and alternative hypotheses symbolically. (c) Explain what it would mean to make a Type I error. (d) Explain what it would mean to make a Type II error. (a) State the null hypothesis in words. Choose the correct answer below. A. The mean price of a single family home in the broker's neighborhood is 243,752. B. The mean price of a single family home in the broker's neighborhood is different from 243,752. C. The mean price of a single family home in the broker's neighborhood is greater than 243,752. D. The mean price of a single family home in any neighborhood is 243,752. State the alternative hypothesis in words. Choose the correct answer below. A. The mean price of a single family home in the broker's neighborhood is different from 243,752. B. The mean price of a single family home in the broker's neighborhood is greater than 243,752. C. The mean price of a single family home in the broker's neighborhood is 243,752. D. The mean price of a single family home in any neighborhood is 243,752.
Transcript text: Three years ago, the mean price of an existing single-family home was $\$ 243,752$. A real estate broker believes that existing home prices in her neighborhood are higher. (a) State the null and alternative hypotheses in words. (b) State the null and alternative hypotheses symbolically. (c) Explain what it would mean to make a Type I error. (d) Explain what it would mean to make a Type II error. (a) State the null hypothesis in words. Choose the correct answer below. A. The mean price of a single family home in the broker's neighborhood is $\$ 243,752$. B. The mean price of a single family home in the broker's neighborhood is different from $\$ 243,752$. C. The mean price of a single family home in the broker's neighborhood is greater than $\$ 243,752$. D. The mean price of a single family home in any neighborhood is $\$ 243,752$. State the alternative hypothesis in words. Choose the correct answer below. A. The mean price of a single family home in the broker's neighborhood is different from $\$ 243,752$. B. The mean price of a single family home in the broker's neighborhood is greater than $\$ 243,752$. C. The mean price of a single family home in the broker's neighborhood is $\$ 243,752$. D. The mean price of a single family home in any neighborhood is $\$ 243,752$.
failed

Solution

failed
failed

Solution Steps

Step 1: State the Null and Alternative Hypotheses in Words

The null hypothesis is a statement that there is no effect or no difference, and it is what we assume to be true until we have evidence to suggest otherwise. In this context, the null hypothesis would be that the mean price of a single-family home in the broker's neighborhood is the same as it was three years ago, which is $\$ 243,752$.

The alternative hypothesis is what the real estate broker believes to be true, which is that the mean price of a single-family home in her neighborhood is higher than $\$ 243,752$.

Step 2: State the Null and Alternative Hypotheses Symbolically

Let \(\mu\) represent the mean price of a single-family home in the broker's neighborhood.

  • Null Hypothesis (\(H_0\)): \(\mu = 243,752\)
  • Alternative Hypothesis (\(H_a\)): \(\mu > 243,752\)
Step 3: Explain What It Would Mean to Make a Type I Error

A Type I error occurs when we reject the null hypothesis when it is actually true. In this context, making a Type I error would mean concluding that the mean price of a single-family home in the broker's neighborhood is higher than $\$ 243,752$, when in fact, it is not.

Final Answer

  • (a) Null Hypothesis in Words: The mean price of a single-family home in the broker's neighborhood is $\$ 243,752$.
  • (b) Symbolic Hypotheses:
    • \(H_0: \mu = 243,752\)
    • \(H_a: \mu > 243,752\)
  • (c) Type I Error Explanation: Concluding the mean price is higher than $\$ 243,752$ when it is not.

\[ \boxed{ \begin{array}{l} \text{(a) Null Hypothesis in Words: A} \\ \text{(b) Symbolic Hypotheses: } H_0: \mu = 243,752, \, H_a: \mu > 243,752 \\ \text{(c) Type I Error Explanation: Concluding the mean price is higher than } \$ 243,752 \text{ when it is not.} \end{array} } \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Refer to Table 4-1. The table above lists the highest prices three consumers, Curly, Moe, and Larry, are willing to pay for a bottle of champagne. If the price of one of the bottles is 95 dollars, total consumer surplus will be 0. 35. 80. 95.
failedAnswered
Burt takes out a loan for 15,000 from his local bank with a simple fixed interest rate of 7.5%. How much interest will he have paid after 8 years? Select one: a. 7100 b. 12,000 c. 24,000 d. 9,000
failedAnswered
Multiple Choice Question When the sympathetic neurons stimulate the adrenal medulla to secrete epinephrine during pain, fear and/or stress, this is an example of a - gland. - substance - neuron - hormone
failedAnswered
All of the following are true about religious symbols/displays on public property EXCEPT the Ten Commandments in the court house are allowed. a) court cases over these issues have been ruled upon under the establishment clause. b) religious displays have been allowed in certain situations. c) displays of a crèche at Christmastime may be allowed if other religious groups are allowed to display their religious symbols and non-secular (religious) displays are also allowed.
failedAnswered
Dr. Baker, a veterinarian, recorded the weight of each newborn kitten her office saw today. Kittens' weights ( g ) What was the interquartile range of the kittens' weights? grams