each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then Round your answers to two decimal places. (a) The sample has size 19, and it is from a normally distributed population with an unknown standard deviation. -0 t = It is unclear which test statistic to use.

Which of the following statements are true?  There may be more than one true statement; check all that are true.   Question 11 options:   a)  The only reason to carry out an observational study instead of an experiment is if we do not have enough money to run the experiment.   b)  The variance of the sample mean depends on the sample size and the population variance.   c)  For large sample sizes, the sample mean will tend to have a normal distribution, whereas for small sample sizes it will tend to have a uniform distribution.   d)  Randomization can be a useful tool in statistical studies, but only for large sample sizes.

You wish to test the following claim (Ha) at a significance level of a = 0.001. H.:µ1 = µ2 Ha:µ1 # µ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal (So use the "pool" option). You obtain the following two samples of data. Sample #1 Sample #2 86.4 60.5 63.3 93.5 94.6 61.1 99.2 55.9 85.8 107 88.9 68.8 88.3 61.9 78.8 59.2 103.8 99.7 74.3 72.5 76.5 62 70.5 80.7 80.2 59.2 64.3 107 89.3 113.2 48.5 95.2 72.1 76.1 115.5 75.1 97.6 88.4 96.4 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the P-value reported from the "2-sample t- test" from the technology you are using. (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a greater than a This test statistic leads…

If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic? Question 3 options: The two samples both have n = 15, with sample variances of 20 and 25. The two samples both have n = 15, with variances of 120 and 125. The two samples both have n = 30, with sample variances of 20 and 25. The two samples both have n = 30, with variances of 120 and 125.