An electrical appliance made by company A has an average life of 2500 hours, with a standard deviation of 500 hours. Another company B makes this appliance with an average life of 2300 hours, and a standard deviation of 800 hours. We take 300 devices from company A and 200 devices from company B. Calculate the probability that the average life of the sample from company A is 100 hours less than the average life of the sample from company B.
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- Linda, a researcher in a technology company, obtained a sample of 270 smartphone owners from California. She wanted to investigate whether Californians were quicker or slower to buy the latest version of a smartphone than the people in the rest of the United States. Linda found the average number of days that Californians waited to buy the latest version of a popular smartphone to be 4. Smartphone owners in the rest of the country typically wait 6 days, with a standard deviation of 21.A prominent medical group claims that the population mean of the surgery durations for all brain tumor patients is 3.69 hours. You are a data analyst for a health insurance company and want to test that claim. To do so, you select a random sample of 32 brain tumor surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all brain tumor surgeries is 1.68 hours. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of the surgery durations for all brain tumor patients. Then state whether the confidence interval you construct contradicts the medical group's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 32 brain tumor patients. (b) (c) Take Sample Sample size: Point estimate: Population standard deviation: Critical value: Compute 0.00 0.00 Number of patients Enter the values…Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 35 minutes and a standard deviation of 3 minutes, while method B has a mean of 39 minutes and a standard deviation of 1.5 minutes. Which procedure is preferred if the procedure must be completed within 34 minutes? Which procedure is preferred if the procedure must be completed within 40.0 minutes? Which procedure is preferred if the procedure must be completed within 43 minutes?
- A sample of size 126 will be drawn from a population with mean 26 and standard deviation 3. Use the TI-84 calculator. Part 1 of 2 Find the probability that x will be between 25 and 27. Round the answer to four decimal places. The probability that x will be between 25 and 27 is Part 2 of 2 th Find the 55 percentile of X. Round the answer to two decimal places. The 55th percentile isSuppose a researcher wants to test if the average diastolic blood pressure in Irish-Americans is different than the average diastolic blood pressure in the general population. Note that the average diastolic blood pressure in the general population is 70 mmHG. The researcher recruits 30 Irish-Americans into this particular study and then measures each of their diastolic blood pressures (mmHG). The population of this sample has a standard deviation equal to 3.0. What is the two-sided alternative hypothesis? (in words) Group of answer choices The mean is different than 70 The mean is different than 73 The mean is greater than 70 The mean is greater than 73Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
- You have obtained the number of years of education from one random sample of 38 police officers from City A and the number of years of education from a second random sample of 30 police officers from City B. The average years of education for the sample from City A is 15 years with a standard deviation of 2 years. The average years of education for the sample from City B is 14 years with a standard deviation of 2.5 years. Is there a statistically significant difference between the education levels of police officers in City A and City B?What is the appropriate test for this case? 2 sample z-testChi-square test 2-sample t-test2 sample paired t-test Carry out the test. The test statistic = (round answer to two decimal places.)and the p-value is (round answer to 2 decimal places)There sufficient evidence at the 5% level to conclude that the education levels of police officers in City A and City B is significantly different.Scientists collect a simple random sample of 25 menthol cigarettes and 25 non-menthol cigarettes. Both samples consist of cigarettes that are filtered, 100mm long, and non-light. The menthol cigarettes have a mean nicotine amount of 0.87 mg and a standard deviation of 0.24 mg. The non-menthol cigarettes have a mean nicotine amount of 0.92 mg and a standard deviation of 0.25 mg. Use a 0.05 significance level to test the claim that non-menthol cigarettes have greater amounts of nicotine than menthol cigarettes. Assume population variances are not equal.The null hypothesis: H, :0 The alternative hypothesis: H :0 The type of test statistic: (Choose one) v The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.05 level of significance: (Round to at least three decimal places.) Can we support the claim that the life expectancy in the United States is greater than the life expectancy in Ireland? O Yes No
- Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, µ, is less than 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 37 hours and that the standard deviation is 3 hours. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H ,) that should be used for the test? H:u is 7 In the context of this test, what is a Type I error? АТурe I error is 7 fact, u is 7 | the hypothesis that µ is ? when, in Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? ?A car company claims that its new SUV gets better gas mileage than its competitor's SUV. A random sample of 49 of its SUVs has a mean gas mileage of 17.1 miles per gallon (mpg). The population standard deviation is known to be 1.3 mpg. A random sample of 33 competitor's SUVS has a mean gas mileage of 16.3 mpg. The population standard deviation for the competitor is known to be 1.6 mpg. Test the company's claim at the 0.05 level of significance. Let the car company be Population 1 and let the competitor be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.According to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Ireland. A new study has been made to see whether this has changed. Records of 235 individuals from the United States who died recently are selected at random. The 235 individuals lived an average of 77.6 years with a standard deviation of 6.7 years. Records of 220 individuals from Ireland who died recently are selected at random and independently. The 220 individuals lived an average of 76.3 years with a standard deviation of 5.5 years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.1 level of significance, is there enough evidence to support the claim that the life expectancy, u,, in the United States is greater than the life expectancy, µ, in Ireland? Perform a one-tailed test. Then fill in the table below. Carry…