MODULE 10: Calculating the Confidence Interval Estimates for Mean µ when a is known Individual work. Directions: Answer the following problem. Round off your answer into three decimal places. (SHOW YOUR SOLUTION) 1. A random sample of size 10 yielded the following observations on the random variable X, the fuel consumption in millions of tons by power plants. Find the point estimate for µ, the mean fuel consumption of power plants. 506 495 508 500 510 515 490 501 508 502

A study asked respondents, "If ever married, how old were you when you first married?" The results are summarized in the technology excerpt that follows. Complete parts (a) through (d) below. One-Sample T: AGEWED Mean Variable StDev SE Mean 99.0% CI AGEWED 26140 23.740 4.668 0.029 (23.666, 23.814) Click the icon to view the table of critical t-values. (a) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval. x = 23.740 (Type an integer or a decimal. Do not round.) E=0.7437 (Type an integer or a decimal. Do not round.) (b) Interpret the confidence interval.

Choose the appropriate statistical test. When computing, be sure to round each answer as indicated. A dentist wonders if depression affects ratings of tooth pain. In the general population, using a scale of 1-10 with higher values indicating more pain, the average pain rating for patients with toothaches is 6.8. A sample of 30 patients that show high levels of depression have an average pain rating of 7.1 (variance 0.8). What should the dentist determine? 1. Calculate the estimated standard error. (round to 3 decimals). [st.error] 2. What is thet-obtained? (round to 3 decimals). 3. What is the t-cv? (exact value) 4. What is your conclusion? Only type "Reject" or Retain"

Also included in question find estimated variance of errors, estimated variance of slope, and 90% and 95% confidence intervals for slope. Thank you so much

Available below are amounts of arsenic in samples of brown rice from three different regions. The amounts are in micrograms of arsenic and all samples have the same serving size. Use a 0.05significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different​ regions? Given that the amounts of arsenic in the samples from region Ahave the highest​ mean, can we conclude that brown rice from region A poses the greatest health​ problem?     Arsenic Amounts (micrograms)                             A 5.8 5.8 6.5 6.5 6.9 7.2 7.3 7.3 7.6 7.6 7.9 7.9   B 4.5 4.9 5.2 5.2 5.5 5.8 5.8 5.9 6.3 6.3 6.4 6.4   C 1.8 3.7 4.1 4.1 4.6 4.6 4.8 5.1 5.2 5.6 5.7 5.7     The Test statistic is:   The P-value is:   The conclusion is: