Given two independent random samples with the following results: n1=12x‾1=108s1=20n1=12x‾1=108s1=20   n2=6x‾2=131s2=26n2=6x‾2=131s2=26 Use this data to find the 95%95% confidence interval for the true difference between the population means. Assume that the population variances are not equal and that the two populations are normally distributed. Copy Data Step 1 of 3:  Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

A sample of n=41n=41 data values randomly selected from a normally distributed population has variance s2=30s2=30. Construct a 95% confidence interval for the population variance. Round your endpoints to one decimal place.

The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed ?2 = 0.18 mm2. An engine inspector took a random sample of 81 fan blades from an engine. She measured each blade and found a sample variance of 0.28 mm2. Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced? (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.00 Find a 90% confidence interval…

Given two independent random samples with the following results: n1=12x‾1=73s1=27n1=12x‾1=73s1=27   n2=12x‾2=102s2=22n2=12x‾2=102s2=22 Use this data to find the 95%95% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.   Step 1 of 3 :   Find the point estimate that should be used in constructing the confidence interval.