### Hypothesis Testing for Airline On-Time PerformanceAn SRS (simple random sample) of 165 flights from a large airline (referred to as airline 1) showed 137 flights were on time. A similar SRS of 165 flights from another large airline (referred to as airline 2) showed 149 flights were on time. Let \( p_1 \) and \( p_2 \) be the proportion of all flights that are on time for airlines 1 and 2, respectively. To determine if airline 2 is more reliable, we check if airline 1 has a lower on-time rate compared to airline 2. Perform the appropriate statistical test at a significance level of 0.02.#### (a) What are the null and alternative hypotheses?- **Null Hypothesis (\( H_0 \))**: \( p_1 < p_2 \)- **Alternative Hypothesis (\( H_A \))**: \( p_1 = p_2 \)#### (b) What is the test statistic?- Fill in your computed test statistic here, rounding your answer to 2 decimal places if needed.#### (c) Using the statistical table, what is the p-value?- Enter the calculated p-value here, rounding your answer to 4 decimal places if needed.#### (d) Based on the p-value, what decision should be made regarding the null hypothesis?- Conclusion: Based on the p-value, **fail to reject** the null hypothesis. This educational example illustrates hypothesis testing using sample data to assess if there is a significant difference in the on-time performance between two airlines at a 0.02 significance level.

Answered: An SRS of 165 flights of a large…

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 psychology graduate student wants to test the claim that there is a significant difference between the IQs of spouses. To test this claim, she measures the IQs of 9 married couples using a standard IQ test. The results of the IQ tests are listed in the following table. Using a 0.10 level of significance, test the claim that there is a significant difference between the IQs assuming that the population distribution of the paired differences is approximately normal. Let the spouse 1 group be Population 1 and let the spouse 2 group be Population 2. Spouse 1 Spouse 2 IQs of Married Couples 124 113 97 123 121 101 128 116 96 126 119 100 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places. 124 111 127 113 107 111
A random sample of n1 = 148 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 14 were found to be high school dropouts. Another random sample of n2 = 125 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 5 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance.
A random sample of n1 = 157 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n2 = 129 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 6 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 42 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,056 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,056 lb42=168 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.3 lb and a standard deviation of 36.8.
A recent study revealed that the average weight of babies born in the United States is normally distributed with a mean of 7.5 pounds. This number is lower than recent years and so researchers are interested in determining what factors are associated with lower birth weights. One researcher decides to look at the age of the mother to determine if younger mothers have babies that are significantly heavier or lighter than average. To study this the researcher collects data from 87 babies who were born to mothers between the ages of 16 and 18. Only one baby was measured per mother. Twins and other multiple births were excluded. The average weight for these babies was 7.3 pounds with a standard deviation of .6 pounds. Was the average weight of babies of young mothers significantly different than babies in the general population? No, the difference was not significant Yes, they were lighter. Yes, they were heavier
An SRS of 190 flights of a large airline (call this airline 1) showed that 160 were on time. An SRS of 190 flights of another large airline (call this airline 2) showed that 172 were on time. Let p1 and P2 be the proportion of all flights that are on time for these two respective airlines. Is airline 2 more reliable? In other words, does airline 1 have a lower on-time rate compared to airline 2? Carry out an appropriate test using a significance level of 0.02. (a) What are the null and alternative hypotheses? Но: р < : 0.0 На р 0.0 (b) What is the test statistic? (Round your answer to 2 decimal places, if needed.) (c) Using the statistical table, what is the p-value? (Round your answer to 4 decimal places, if needed.) (d) Based on the p-value, fail to reject + the null hypothesis.
A researcher believes that among the residents of a remote community, 30% have type O blood, 50% have type A blood, 10% have type B blood and 10% have type AB blood. She takes a random sample of 80 residents and finds that 20 had type O blood, 40 had type A blood, 12 had type B blood and 8 had type AB blood. Do the data follow the hypothesized distribution of blood type for this community? Test at a = .05. Round your answers to three decimal places, if necessary. Null hypothesis: Ho: Po = 0.3, PA = 0.5, PB = 0.1, PAB = 0.1 20 40 12 8 80 80 80 80 1 1 1 20 40 8 Ho: Po = Ho: Po = Alternative hypothesis: Ho: Po = PA = PB = PAB = Ha: po # Type O 1 Ha: Po PA PB = PAB = 4 20 › PA = PA = Type 0 20 24 40 80 80 Ha: Po 0.3, PA # 0.5, PB At least one of the proportions is different. Complete the table of observed counts: Type O , PA # 0.667 Type A PB = PB = 40 Type A 40 What is the test statistic? 2.667 1 ,PB # 0 , PAB = 1 12¹ PAB Complete the table of expected counts under the null hypothesis: 12…
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 42 passengers, and a flight has fuel and baggage that allows for the total passenger load of 6,972lb. The pilot sees that the plane is full and all the passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,972lb/42=166lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that the weights of men are normally distributed with a mean of 176.9lb and a standard deviation of 37.7. THE probability is approximately. ? Round to four decimal places.
Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 7 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.4 hours with a standard deviation of 0.3 hours. For a random sample of 6 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.2 hours to paint each room with a standard deviation of 0.2 hours. At the 0.05 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using…
Clothes dried outside smell better than those dried in a dryer because of a process called photolysis. Sunlight breaks down compounds that cause odor. A trained smeller is asked to smell a random sample of 20 towels. The smeller does not know it, but all of the 20 towels have been dried in the sun. The smeller is blindfolded and is not allowed to touch the towels but leans forward to smell the towel then rates the towel on a smell-scale of 1 to 10, where 1 is the an extremely unpleasant smell and 10 is a very good smell. A smell rating of 8 is typically attributed to a towel that is dried in the dryer. The mean smell rating for these 20 towels is approximately normal with a mean of 8.45 and the standard deviation is 0.887. A statistician performs a test of Ho μ = 8 versus H₁ μ> 8 where is the true mean smell rating for all towels dried in the sun. This test yields a P-value of 0.0176. What conclusion would you make at the significance level a = 0.05? Because the P-value of 0.0176 < α =…
At a local food processing plant, it used to take an average of 90 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes. A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on the new machine. It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7 minutes. Use a significance level of 0.01 to test the claim that the mean time is different from 90 minutes. What is the decision? A) Reject Ho because the test statistic is in the critical region and the p-value is greater than the significance level. B) Reject Ho because the test statistic is not in the critical region and the p-value is greater than the significance level.…
At a local food processing plant, it used to take an average of 90 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes. A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on the new machine. It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7 minutes. Use a significance level of 0.01 to test the claim that the mean time is different from 90 minutes. What is the test statistic? A) -7.01 B) -2.539 C) -3.19 D) -2.528 E) -1.96

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