### Hypothesis Testing on Mean Daily High TemperatureThe National Weather Service states that the mean daily high temperature for October in a large Midwestern city is \( 57^\circ F \). A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean is actually lower than \( 57^\circ F \). ### Given Data- Sample Mean (\(\bar{X}\)): \( 55^\circ F \)- Population Standard Deviation (\(\sigma\)): \( 5.7^\circ F \)- Significance Level (\(\alpha\)): 0.01We want to perform the hypothesis test at the \(\alpha = 0.01\) significance level.### Hypothesis Statements1. Greater than \(57^\circ F\): - Null Hypothesis (\(H_0\)): \( \mu = 57^\circ F \) - Alternative Hypothesis (\(H_a\)): \( \mu > 57^\circ F \) - Test statistics: \( z = -1.92 \) - Critical Value: \( z = -2.33 \) - Conclusion: Fail to reject \(H_0: \mu = 57^\circ F\). There is not sufficient evidence to support the claim that the mean is greater than \(57^\circ F\).2. Less than \(57^\circ F\): - Null Hypothesis (\(H_0\)): \( \mu = 57^\circ F \) - Alternative Hypothesis (\(H_a\)): \( \mu < 57^\circ F \) - Test statistics: \( z = -1.92 \) - Critical Value: \( z = -2.33 \) - Conclusion: Fail to reject \(H_0: \mu = 57^\circ F\). There is not sufficient evidence to support the claim that the mean is less than \(57^\circ F\).### SummaryFor both hypothesis tests, the test statistics provided (\(z = -1.92\)) is compared against the critical value (\(z = -2.33\)). In both cases, the null hypothesis is not rejected, indicating insufficient evidence to support either of the alternative hypotheses regarding the mean daily high temperatures differing from \( 57^\circ F \).

Name: ### Hypothesis Testing on Mean Daily High TemperatureThe National Wea
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: ### Hypothesis Testing on Mean Daily High TemperatureThe National Weather Service states that the mean daily high temperature for October in a large Midwestern city is \( 57^\circ F \). A local weather service suspects that this value is not accurat

Given that Claim : Mean is actually lower than 570F . Sample size(n) = 30 Sample mean = 550F…

Math

Statistics

The National Weather Service says that the mean daily high temperature for October in a large Midwestern city is 57°F. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean is actually lower than 57°FA sample of mean daily high temperatures for October over past 30 years yields X = 55° F Assume that the population standard deviation is 5.7°F. Perform the hypothesis test at the a = 0.01 significance level. %3D

The National Weather Service says that the mean daily high temperature for October in a large Midwestern city is 57°F. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean is actually lower than 57°FA sample of mean daily high temperatures for October over past 30 years yields X = 55° F Assume that the population standard deviation is 5.7°F. Perform the hypothesis test at the a = 0.01 significance level. %3D

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A simple random sample of 46 men from a normally distributed population results in a standard deviation of 9.6 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below.
A simple random sample of 49 men from a normally distributed population results in a standard deviation of 7.8 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: o = 10 beats per minute B. Ho: o+ 10 beats per minute H1: o< 10 beats per minute H1: o = 10 beats per minute O C. Ho: o2 10 beats per minute D. Ho: o = 10 beats per minute H1: o< 10 beats per minute H: o + 10 beats per minute b. Compute the test statistic. (Round to three decimal places as needed.) c. Find the P-value. P-value = (Round to four decimal places as needed.) d.…
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 4.4 lbs/square inch. Assume the standard deviation is known to be 0.9. If the valve was designed to produce a mean pressure of 4.5 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? State the null and alternative hypotheses for the above scenario.
A simple random sample of 30 men from a normally distributed population results in a standard deviation of 8.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range , the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts a through d below . b. Compute the test statistic. x^2 =____ ( round to three decimal places as needed ) c. Find the p value ___ ( round to four decimal places as needed ) . d. State the conclusion
A simple random sample of 42 men from a normally distributed population results in a standard deviation of 9.9 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. a. Compute the test statistic. chi squared equals (Round to three decimal places as needed.) b. Find the P-value. P-valueequals (Round to four decimal places as needed.)
A simple random sample of 43 men from a normally distributed population results in a standard deviation of 11.1 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below.
A simple random sample of 49 men from a normally distributed population results in a standard deviation of 10.5 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below. TTounu U uree uetima piates as ieeueu.) c. Find the P-value. P-value = | (Round to four decimal places as needed.)
A simple random sample of 46 men from a normally distributed population results in a standard deviation of 7.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below. Question content area bottom Part 1 a. Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: σ≥10 beats per minute H1: σ<10 beats per minute B. H0: σ≠10 beats per minute H1: σ=10 beats per minute C. H0: σ=10 beats per minute H1: σ<10 beats per minute D. H0: σ=10 beats per minute H1: σ≠10 beats per minute Your answer is correct. Part 2 b. Compute the test statistic.…
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 140 engines and the mean pressure was 6.8 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 6.9 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.
A simple random sample of 46 men from a normally distributed population results in a standard deviation of 7.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below. Question content area bottom Part 1 a. Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: σ≥10 beats per minute H1: σ<10 beats per minute B. H0: σ≠10 beats per minute H1: σ=10 beats per minute C. H0: σ=10 beats per minute H1: σ<10 beats per minute D. H0: σ=10 beats per minute H1: σ≠10 beats per minute Your answer is correct. Part 2 b. Compute the test statistic.…
A simple random sample of 41 men from a normally distributed population results in a standard deviation of 8.1 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. test statistic_____ pvalue______
A simple random sample of 42 men from a normally distributed population results in a standard deviation of 8.4 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below. O A. Ho: o 10 beats per minute O B. Ho: 0= 10 beats per minute H:g< 10 beats per minute H,:o<10 beats per minute OC. Ho: o = 10 beats per minute O D. Ho: o+ 10 beats per minute H,:0 = 10 beats per minute H,:0# 10 beats per minute b. Compute the test statistic. (Round to three decimal places as needed.) c. Find the P-value. P-value = (Round to four decimal places as needed.) d. State the conclusion. Ho, because the P-value is V the level of significance. There is…