4. A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho : µ =12 against H1:µ< 12, using a random sample of four specimens. What is the type I error probability if the critical region is defined as x < 11.5 kilograms?
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- Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.01 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. City #1 City #2101 11786 59121 100118 85101 82104 107213 110133 111290 120100 133255 101145 209Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.01 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents.Complete parts (a) and (b) below. City #1 City #2101 11786 62121 100111 85101 90104 107213 110100 111290 149100 133272 101145 209 a. What are the null and alternative hypotheses? The test statistic, t, is The P-value is State the conclusion for the test. b. Construct a confidence interval suitable for testing the claim that the mean amount of strontium-90 from city #1…Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.10 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. a. The test statistic is (Round to two decimal places as needed.) b. The P-value is (Round to three decimal places as needed.)
- Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.100.10 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents.Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. Click the icon to view the data table of strontium-90 amounts. a. The test statistic is (Round to two decimal places as needed.) b. The P-value is (Round to three decimal places as needed.)Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. a. The test statistic is (Round to two decimal places as needed.) b. The P-value is (Round to three decimal places as needed.)
- Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. City_#1 City_#2 102 117 86 53 121 100 116 85 101 89 104 107 213 110 114 111 290 115 100 133 281 101 145 209 A. Find test statistic. (Round to two decimal places.) B. Find P-Value. (Round to three decimal places.) C. Is the conclusion affected by whether the significance by whether significance level is 0.10 or 0.01?Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. City_#1 City_#2108 11786 53121 100116 85101 83104 107213 110113 111290 142100 133266 101145 209 What are the null and alternative hypotheses? Assume that population 1 consists of amounts from city #1 levels and population 2 consists of amounts from city #2? The test statistic is? The P-value is? State the conclusion for the test?Listed in the data table are amounts of strontium-90 (in millibrcquerels or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.10 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. Find the test statistic, p value, and confidence interval
- If conducting a two-sided test at level of significance 0.05 based on a sample of size 20, the critical t-value is ?Find the t values that form the boundaries of the critical region for a two-tailed test with α = 0.02 for a sample size of 19.The article “Wind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulating Foam Adhesive” (P. Datin, D. Prevatt, and W. Pang, Journal of Architectural Engineering, 2011:144–154) presents a study of the failure pressures of roof panels. A sample of 15 panels constructed with 8-inch nail spacing on the intermediate framing members had a mean failure pressure of 8.38 kPa with a standard deviation of 0.96 kPa. A sample of 15 panels constructed with 6-inch nail spacing on the intermediate framing members had a mean failure pressure of 9.83 kPa with a standard deviation of 1.02 kPa. Can you conclude that 6-inch spacing provides a higher mean failure pressure?
