On their website, a property management company states that the mean monthly rent for apartments on the east side of town is $700. A researcher for a consumer advocacy group believes that, due to the construction of newer apartment complexes in neighboring towns, the mean monthly rent on the east side, u, is now lower. A random sample of 22 monthly rents for apartments on the east side has a mean of $696, with a standard deviation of $17. Assume that current monthly rents for apartments on the east side are approximately normally distributed. Based on the sample, is there enough evidence to conclude, at the 0.05 level of significance, that the population mean monthly rent is now less than what is stated on the website? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. HO (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) H Xx ☐☐ O S 2 OSO □ロ p p ☐ ロマロ >O
On their website, a property management company states that the mean monthly rent for apartments on the east side of town is $700. A researcher for a consumer advocacy group believes that, due to the construction of newer apartment complexes in neighboring towns, the mean monthly rent on the east side, u, is now lower. A random sample of 22 monthly rents for apartments on the east side has a mean of $696, with a standard deviation of $17. Assume that current monthly rents for apartments on the east side are approximately normally distributed. Based on the sample, is there enough evidence to conclude, at the 0.05 level of significance, that the population mean monthly rent is now less than what is stated on the website? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. HO (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) H Xx ☐☐ O S 2 OSO □ロ p p ☐ ロマロ >O
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 8SGR
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Question
18
![**Title: Hypothesis Testing for Mean Monthly Rent**
On their website, a property management company states that the mean monthly rent for apartments on the east side of town is $700. A researcher for a consumer advocacy group believes that, due to the construction of newer apartment complexes in neighboring towns, the mean monthly rent on the east side, \( \mu \), is now lower. A random sample of 22 monthly rents for apartments on the east side has a mean of $696, with a standard deviation of $17.
Assume that current monthly rents for apartments on the east side are approximately normally distributed. Based on the sample, is there enough evidence to conclude, at the 0.05 level of significance, that the population mean monthly rent is now less than what is stated on the website?
**Perform a one-tailed test. Then complete the parts below:**
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
- **(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \):**
\( H_0: \) [ ]
\( H_1: \) [ ]
- **(b) Determine the type of test statistic to use:**
\[ \text{Choose one: } \left[ \text{ } \right] \]
- **(c) Find the value of the test statistic. (Round to three or more decimal places.)**
\[ \text{Test Statistic: } \left[ \right] \]
- **(d) Find the p-value. (Round to three or more decimal places.)**
\[ \text{p-value: } \left[ \right] \]
- **(e) Can we conclude that the mean monthly rent for apartments on the east side is less than what is stated on the website?**
\[ \text{Yes } \left[ \right] \text{ No } \left[ \right] \]
This exercise illustrates a typical hypothesis test for a mean, using statistical concepts such as test statistics, p-values, and significance levels. It involves identifying null and alternative hypotheses, determining appropriate test statistics, calculating values, and making conclusions based on statistical evidence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5db6d82f-0d7b-4a27-9056-ef6822baa75c%2Ff85298e4-f5a7-405d-bfba-16b81a5ba964%2Fqh7m46q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Hypothesis Testing for Mean Monthly Rent**
On their website, a property management company states that the mean monthly rent for apartments on the east side of town is $700. A researcher for a consumer advocacy group believes that, due to the construction of newer apartment complexes in neighboring towns, the mean monthly rent on the east side, \( \mu \), is now lower. A random sample of 22 monthly rents for apartments on the east side has a mean of $696, with a standard deviation of $17.
Assume that current monthly rents for apartments on the east side are approximately normally distributed. Based on the sample, is there enough evidence to conclude, at the 0.05 level of significance, that the population mean monthly rent is now less than what is stated on the website?
**Perform a one-tailed test. Then complete the parts below:**
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
- **(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \):**
\( H_0: \) [ ]
\( H_1: \) [ ]
- **(b) Determine the type of test statistic to use:**
\[ \text{Choose one: } \left[ \text{ } \right] \]
- **(c) Find the value of the test statistic. (Round to three or more decimal places.)**
\[ \text{Test Statistic: } \left[ \right] \]
- **(d) Find the p-value. (Round to three or more decimal places.)**
\[ \text{p-value: } \left[ \right] \]
- **(e) Can we conclude that the mean monthly rent for apartments on the east side is less than what is stated on the website?**
\[ \text{Yes } \left[ \right] \text{ No } \left[ \right] \]
This exercise illustrates a typical hypothesis test for a mean, using statistical concepts such as test statistics, p-values, and significance levels. It involves identifying null and alternative hypotheses, determining appropriate test statistics, calculating values, and making conclusions based on statistical evidence.
Expert Solution
Step 1
Given populations mean μ=700, sample standard deviations=17, n=sample size=22, sample mean x̄=696, level of significance ɑ=0.05
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