Obtain an 80% confidence interval for the difference in proportions of women in these two engineering fields
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A: It is given that x̄1 = 290 x̄2 = 321 s1 = 12 s2 = 22 n1 = 10 n2 = 16
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10 engineering schools were surveyed. The first random sample of 250
electrical engineers had 80 women, and the second random sample of 175
chemical engineers had 40 women. Obtain an 80% confidence interval for the
difference in proportions of women in these two engineering fields
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- The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,069 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 171 of their customers and calculates that these customers used an average of 10,461 kWh of electricity last year. Assuming that the population standard deviation is 2973 kWh, is there sufficient evidence to support the power company's claim at the 0.01 level of significance? Step 3 of 3: Draw a conclusion and interpret the decision.In a random sample of males, it was found that 29 write with their left hands and 212 do not. In a random sample of females, it was found that 70 write with their left hands and 444 do not. Use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below.Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on arganisms, an expert claimed that the amount of gamma radiation needed to sterilize a colany of tardigrades no longer has a mean of 1200 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A study was conducted on a sample of 21 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean af 1225 Gy, with a sample standard deviation of 65 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level af significance, to support the claim that H, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is nat equal to 1200 Gy. (a) State the null hypothesis and the…
- The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,069 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 171 of their customers and calculates that these customers used an average of 10,461 kWh of electricity last year. Assuming that the population standard deviation is 2973 kWh, is there sufficient evidence to support the power company's claim at the 0.01 level of significance? Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.In a previous poll, 39% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 422 of 1145 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the x = 0.01 significance level. Because npo (1-Po) = 272.4 > 10 and the sample size is the hypothesis are satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? Ho: P = versus H₁: ▼ V (Type integers or decimals. Do not round.) Find the test statistic, Zo- C less than 5% of the population size, and the sample is given to be random, the requirements for testing Zo = (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Is there sufficient…Fifteen years ago, a complete survey of all undergraduate students at a large University indicated that the average student smoked 7.7 cigarettes per day. Th director of the student health center wishes to determine whether the incidence of cigarette smoking at his University has lessened over the fifteen year period. He obtains the following results (in cigarettes smoked per day) from a random sample of 9 students. 6.1, 9.2, 5, 6.3, 4.8, 3.2, 7.6, 8.1, 9. Test the null hypothesis at the .05 level significane.
- A cell phone manufacturer tests the battery lifetimes of its cell phones by recording the time it takes for the battery charges to run out while testers are streaming videos on the phones continuously. The manufacturer claims that the population mean of the battery lifetimes of all phones of their latest model is 5.26 hours. As a researcher for a consumer information service, you want to test that claim. To do so, you select a random sample of 45 cell phones of the Español manufacturer's latest model and record their battery lifetimes. Assume it is known that the population standard deviation of the battery lifetimes for that cell phone model is 2.42 hours. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. Then state whether the confidence interval you construct contradicts the manufacturer's claim. (If necessary, consult a list of formulas.) 00 (a)…n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 n x=0.05 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 0.553 0.532 0.514 0.497 0.482 0.468 0.456 0.444 0.396 0.361 0.335 0.312 0.294 0.279 0.254 0.236 0.220 0.207 0.196 α = 0.05 α = 0.01 0.990 0.959 0.917 0.875 0.834 0.798 0.765 0.735 0.708 0.684 0.661 0.641 0.623 0.606 0.590 0.575 0.561 0.505 0.463 0.430 0.402 0.378 0.361 0.330 0.305 0.286 0.269 0.256 α = 0.01 NOTE: To test Ho: p=0 against H₁: p0, reject Ho if the absolute value of ris greater than the critical value in the table.Consider two sets of data, X and Y, with n = 10 observations each. If the mean ranks for X and Y are 6 and 5, respectively, what is the test statistic for the Wilcoxon Signed-Ranks test on these two sets of data?
- Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in ₁ = 290 and ₁ = 12, and another random sample of 16 gears from the second supplier results in ₂ = 321 and s₂ = 22. Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use a = 0.05, and assume that both populations are normally distributed but the variances are not equal. a. Because -4.64 < -1.714, reject the Null Hypothesis b. Reject the Null Hypothesis c. Because -4.64 < -1.714, fail to reject the Null Hypothesis O d. None among the choicesThe Substance Abuse and Mental Health Services Administration (SAMHSA, 2017) estimates that 10.9% of the population of the United States age 18–24 had an episode of depression in the previous 12 months. Suppose a researcher takes a random sample of 225 United States adults aged 18–24. Determine the value of the sample proportion, p, such that 5% of samples of 225 United States adults age 18–24 are greater than p. You may find software or a z-table useful. Give your answer precise to three decimal places. p = IIThe news release referenced in the previous exercise also included data fromindependent samples of teenage drivers and parents of teenage drivers. In response to aquestion asking if they approved of laws banning the use of cell phones and texting whiledriving, 74% of the teens surveyed and 95% of the parents surveyed said they approved.The sample sizes were not given in the news release, but suppose that 600 teens and 400 parents of teens were surveyed and that these samples are representative of the twopopulations. Do the data provide convincing evidence that the proportion of teens whoapprove of banning cell phone and texting while driving is less than the proportion ofparents of teens who approve?