A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26 temperature readings gave a sample variance of 4.2. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.2. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.) (a) What is the level of significance? State the null and alternate hypotheses. H0: ?12 = ?22; H1: ?12 ≠ ?22H0: ?12 > ?22; H1: ?12 = ?22 H0: ?12 = ?22; H1: ?12 > ?22H0: ?12 = ?22; H1: ?12 < ?22 (b) Find the value of the sample F statistic. (Round your answer to two decimal places.) What are the degrees of freedom? dfN = dfD = What assumptions are you making about the original distribution? The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions. The populations follow independent chi-square distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population. (c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.) p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.

A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26 temperature readings gave a sample variance of 4.2. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.2. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.) (a) What is the level of significance? State the null and alternate hypotheses. H0: ?12 = ?22; H1: ?12 ≠ ?22H0: ?12 > ?22; H1: ?12 = ?22 H0: ?12 = ?22; H1: ?12 > ?22H0: ?12 = ?22; H1: ?12 < ?22 (b) Find the value of the sample F statistic. (Round your answer to two decimal places.) What are the degrees of freedom? dfN = dfD = What assumptions are you making about the original distribution? The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions. The populations follow independent chi-square distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population. (c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.) p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.

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Description: A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?₁² = ?₂²; H₁: ?₁² ≠ ?₂²H₀: ?₁² > ?₂²; H₁: ?₁² = ?₂² H₀: ?₁² = ?₂²; H₁: ?₁² > ?₂²H₀: ?₁² = ?₂²; H₁: ?₁² < ?₂²

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

df_N	=
df_D	=

What assumptions are you making about the original distribution?

The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions. The populations follow independent chi-square distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.

p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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