### Statistical Analysis of Laptop Replacement TimesThe manager of a computer retail store suspects that the laptops he receives from suppliers are of lower quality than average. According to his research, the replacement times for a particular model are normally distributed, with a mean of 4.5 years and a standard deviation of 0.5 years. He analyzes records of 49 laptops and discovers the mean replacement time is 4.4 years.#### Objective:Calculate the probability that the mean replacement time for 49 randomly selected laptops is 4.4 years or less.### Calculation:Given:- Population mean (μ) = 4.5 years- Standard deviation (σ) = 0.5 years- Sample size (n) = 49The probability question is:\[ P(M \le 4.4 \text{ years}) = \, \_ \]Enter your answer accurate to 4 decimal places, using either exact z-scores or z-scores rounded to 3 decimal places.### Decision:- **Question:** Based on the probability calculated, does it seem that laptops of lower quality than average are being supplied? - **Option 1:** Yes. The probability of this data is unlikely to have occurred by chance alone. - **Option 2:** No. The probability of obtaining this data is high enough to have been a chance occurrence. Use statistical analysis to determine the quality inference about the laptops.

The random variable replacement time follows normal distribution. The population mean is 4.5 and…

Answered: The manager of a computer retails store…

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 researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 2.4 micrograms/mL, for a level of significance of 1%, what should the researcher’s decision rule look like? Reject H0 if z is less than or equal to –2.326. Reject H0 if z is greater than or equal to 2.326. Reject H0 if z is less than or equal to –2.576. Reject H0 if z is greater than or equal to 2.5760
A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 2.4 micrograms/mL, for a level of significance of 1%, what should the researcher’s decision rule look like? Reject H0 if z is less than or equal to –2.326. Reject H0 if z is greater than or equal to 2.326. Reject H0 if z is less than or equal to –2.576. Reject H0 if z is greater than or equal to 2.5760
A company that runs a chain of quick oil change centers, tries to attract customers by claiming that it completes oil changes faster than its competition. So it periodically estimates the time taken to do oil changes at its centers. From historical records, the company knows that the population standard deviation of oil change duration is 15 minutes. Recently, 40 customers were asked how much time they spent getting an oil change at one of their centers. Based on the sample data, the chain concluded that the average oil change time for the population of all its customers was between 15 and 25 minutes. What was the confidence level at which the inference was made?
The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1775 pounds and a standard deviation of 60 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1775 pounds. To see if this is the case, 90 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1788 pounds. Can we support, at the 0.05level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1775 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. a. State the null hypothesis H0 and the alternative hyposthesis H1. b. Find the value of the test statistic. c. Find the p-value. d. Can we…
Suppose that water usages in American showers are normally distributed, with an average shower using 20 gallons, and a standard deviation of 3.2 gallons. Estimate the percentage of showers that used (a) between 13.6 and 26.4 gallons. % (b) more than 26.4 gallons. % (c) less than 10.4 gallons. % (d) between 16.8 and 29.6 gallons. %
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A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 2.4 micrograms/mL, for a level of significance of 1%, what should the researcher’s decision rule look like?
The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1800 pounds and a standard deviation of 90 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1800 pounds. To see if this is the case, 100 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1818 pounds. Can we support, at the 0.05 level of significance, the claim that the population mean breaking strength of the newly- manufactured cables is greater than 1800 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H :O 1 (b) Determine the…
A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 2.4 micrograms/mL, for a level of significance of 1%, what should the researcher’s decision rule look like? Reject H0 if z is less than or equal to –2.326. Reject H0 if z is greater than or equal to 2.326. Reject H0 if z is less than or equal to –2.576. Reject H0 if z is greater than or equal to 2.5760
A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 2.4 micrograms/mL, for a level of significance of 1%, what should the researcher’s decision rule look like? Reject H0 if z is less than or equal to –2.326. Reject H0 if z is greater than or equal to 2.326. Reject H0 if z is less than or equal to –2.576. Reject H0 if z is greater than or equal to 2.5760

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