### Problem StatementAn electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 45 bulbs has an average life of 710 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm.- Click here to view page 1 of the standard normal distribution table.- Click here to view page 2 of the standard normal distribution table.- Click here to view page 1 of the table of critical values of the t-distribution.- Click here to view page 2 of the table of critical values of the t-distribution.### SolutionThe confidence interval is [ ___ ] < μ < [ ___ ].(Round to the nearest integer as needed.) **Determining Sample Size for Confidence in Mean Lifespan of Light Bulbs**An electrical firm manufactures light bulbs that have a lifespan approximately normally distributed with a standard deviation of 40 hours. To ensure the sample mean is within 14 hours of the true mean with 94% confidence, calculate the necessary sample size.- [View page 1 of the standard normal distribution table](#)- [View page 2 of the standard normal distribution table](#)- [View page 1 of the table of critical values of the t-distribution](#)- [View page 2 of the table of critical values of the t-distribution](#)---**Solution:**The required sample size is [ _ ]. (Note: Round up to the nearest whole number as needed.)

Let X be the length of a light bulb.Given,

Answered: An electrical firm manufactures light…

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 random sample of size n, = 21, taken from a normal population with a standard deviation o, = 5, has a mean x1 = 87. A second random sample of size n= 38. taken from a different normal population with a standard deviation o, = 3, has a mean x2 = 33. Find a 94% confidence interval for u, - u,. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The confidence interval is (Round to one decimal place as eeded.) Enter your answer in the edit fields and then click Check Answer. All parts showing Clear All Check Answer US 9 3:02 acer % & peq 7 8. 9.
A newly developed vaccine has been developed and the vaccine has to be kept very cold so it is effective. If the temperature of the stored vaccine vials raises above 40 degree Fahrenheit the vials can no longer be used. The freezer at the pharmacy of a small town is old and the temperature fluctuates following a normal distribution with mean μ and standard deviation 5. The pharmacist can set μ to a preferred temperature. If the pharmacist wants to guarantee that the vials are damaged with probability no higher than 0.02, what is the highest µ that she can set? Enter your answer to 2 decimal points. (Standard Normal Table)
It takes an average of 9.8 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will change if the patient is immediately told the truth about the injury. The EMT randomly selected 52 injured patients to immediately tell the truth about the injury and noticed that they averaged 10.7 minutes for their blood to begin clotting after their injury. Their standard deviation was 1.98 minutes. What can be concluded at the the αα = 0.05 level of significance? For this study, we should use Select an answer t-test for a population mean, z-test for a population proportion The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer = ≠ < > H1:H1: ? p μ Select an answer < ≠ > = The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject fail to reject accept…
A sample of 10 from population 1 has a mean of 32 and a standard deviation of 6. A sample of 13 from population 2 has a mean of 48 and a standard deviation of 8. The population standard deviations are unknown but assumed to be equal. Test the hypothesis, at the 1% level of significance, that the population means are the same. State your conclusion as a sentence and include the test statistic and the critical value.
An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 35 hours. If a sample of 45 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. |<µ<. (Round to the nearest integer as needed.) The confidence interval is
A chain of restaurants has historically had a mean wait time of 5 minutes for its customers. Recently, the restaurant added several very popular dishes back to their menu. Due to this, the manager suspects the wait time, μ, has increased. He takes a random sample of 35 customers. The mean wait time for the sample is 5.1 minutes. Assume the population standard deviation for the wait times is known to be 1.1 minutes. Can the manager conclude that the mean wait time is now greater than 5 minutes? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho: O H₁:0 μ X 0° OO 20ם ローロ OO × 5 (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. 0.10 is the value that cuts off an area of 0.10 in the right tail. *-μ ⚫ The test statistic has a normal distribution and the value is given by z=- σ √n Standard Normal…
It takes an average of 14.5 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will increase if the patient is immediately told the truth about the injury. The EMT randomly selected 65 injured patients to immediately tell the truth about the injury and noticed that they averaged 15.4 minutes for their blood to begin clotting after their injury. Their standard deviation was 3.05 minutes. What can be concluded at the the αα = 0.05 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton mean is significantly greater than 14.5 at αα = 0.05, so there is statistically significant…
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It takes an average of 12.7 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will decline if the patient is immediately told the truth about the injury. The EMT randomly selected 51 injured patients to immediately tell the truth about the injury and noticed that they averaged 12.4 minutes for their blood to begin clotting after their injury. Their standard deviation was 3.77 minutes. What can be concluded at the the αα = 0.10 level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: H0:H0: ? p μ Select an answer > < ≠ = H1:H1: ? p μ Select an answer = < ≠ > The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject accept fail to reject…
A coin-operated drink machine was designed to discharge a mean of 7 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 9 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.77 fluid ounces and 0.27 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 7 fluid ounces? Use the 0.10 level of significance. Perform a two-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. H₁ : μ = 7 H₁ μ‡7 (b) Determine the type of test statistic to use. Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) t (d) Find the p-value. (Round to three or…

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