(a) Use Table C or software to find the critical value t* for a 90% confidence interval for the mean of the population based on n = 2 observations. O 1.645 O 2.920 O 6.314 O 3.078 (b) Use Table C or software to find the critical value t* for a 95% confidence interval for the mean of the population from an SRS of 20 observations. 2.093 O 1.729 O 1.960 2. 086

4. The resilient moduli of 10 samples of a clay mixture are measured and the sample mean is x = 19.50. If an experimenter wishes to use a "known" value o = 1.0 for the standard deviation of the resilient modulus measurements based upon prior experience, construct appropriate 90%, 95%, and 99% two-sided confidence intervals for the average resilient modulus µ. Compare the lengths of the confidence intervals. Do you think it is plausible that the average resilient modulus is equal to 20.0?

Determine whether the following statements are True or False: In a confidence interval (CI) for a population mean, the margin of error (MOE) is half the width of the CI. If we constructed 1000 independent 90% CI’s for a population mean µ, thenwe’d expect about 900 of them to contain µ If we increase the sample size of SRS’s, then the width of the CI’s corresponding to the SRS’s decreases, i.e., the CI’s become narrower

One method for measuring air pollution is to measure the concentration of carbon monoxide, or CO, in the air. Suppose Nina, an environmental scientist, wishes to estimate the CO concentration in Zagreb, Croatia. She randomly selects 45 locations throughout the city measures the CO concentration at each location. Based on her 45 samples, she computes the margin of error for a 95% t-confidence interval for the mean concentration of CO in Zagreb, in µg/m³, to be 4.28. What would happen to the margin of error if Nina decreases the confidence level to 90%? Nina increases the confidence level to 99%? Nina decreases the sample size to 33 locations? Nina increases the sample size to 65 locations? Answer Bank Increase Stay the same Decrease

6.2.3 Find the critical value t, for the confidence levelc=0.99 and sample size n= 12. Click the icon to view the t-distribution table. (Round to the nearest thousandth as needed.)

Assume that all​ grade-point averages are to be standardized on a scale between 0 and 6. How many​ grade-point averages must be obtained so that the sample mean is within 0.005 of the population​mean? Assume that a 99​% confidence level is desired. If using the range rule of​ thumb, σ can be estimated as range4=6−04=1.5. Does the sample size seem​ practical?

Assume that all​ grade-point averages are to be standardized on a scale between 0 and 6. How many​ grade-point averages must be obtained so that the sample mean is within 0.012 of the population​ mean? Assume that a 95​% confidence level is desired. If using the range rule of​ thumb, σ can be estimated as range/4=6−0/4=1.5. Does the sample size seem​ practical?