Tyler and Jack are both studying a numerical variable X. Both students want to estimate the population mean of this variable, and they each intend to collect a sample, calculate a sample mean and construct a 95% confidence interval. Each student will collect their own sample, but both samples will have 3i] items in them. when constructing his confidence interval, Tyler assumes a value for the population standard deviation, o. In contrast, Jack does not assume a value for the population standard deviation. Jack calculates the sample standard deviation, 5, and uses this in his condence interval. As it turns out, the sample standard deviation that Jack calculates turns out to be slightly less than the value assumed by Tyler for the population standard deviation. Based on this information, it is true to savr that: both confidence intervals will be of the same width it is impossible to tell which condence interval will be wider Tyler's confidence interval will be wider than Jack's Jack's confidence interval will be wider than Tyler's OOOO Critical Values of t (1-tailed probabilities) Degrees of freedom t.100 t.050 t.025 t.010 t.005 1 3.0777 6.3138 12.7062 31.8207 63.6574 2 1.8856 2.9200 4.3027 6.9646 9.9248 3 1.6377 2.3534 3.1824 4.5407 5.8409 4 1.5332 2.1318 2.7764 3.7469 4.6041 5 1.4759 2.0150 2.5706 3.3649 4.0322 6 1.4398 1.9432 2.4469 3.1427 3.7074 7 1.4149 1.8946 2.3646 2.9980 3.4995 8 1.3968 1.8595 2.3060 2.8965 3.3554 9 1.3830 1.8331 2.2622 2.8214 3.2498 10 1.3722 1.8125 2.2281 2.7638 3.1693 11 1.3634 1.7959 2.2010 2.7181 3.1058 12 1.3562 1.7823 2.1788 2.6810 3.0545 13 1.3502 1.7709 2.1604 2.6503 3.0123 14 1.3450 1.7613 2.1448 2.6245 2.9768 15 1.3406 1.7531 2.1315 2.6025 2.9467 16 1.3368 1.7459 2.1199 2.5835 2.9208 17 1.3334 1.7396 2.1098 2.5669 2.8982A medical team is studying the the ramifications of obesity in society. As part of this study, a controi group of 26 people has been collected, and the resting heart rates [in beats per minute) has been measured in these subjects. The average heart rate in this control group is 77.2. The sample standard dewation for this group is 3.9. Calculate the 90% condence interval for the mean heart rate in the population. You may nd this Student's t distribution table useful. Give your answers to 2 deCimal places