Question

Refer to slide 11 in the PowerPoint deck 13. Look at the examples below and determine whether the conditions for the estimation of the mean are met, and if so, whether it is appropriate to look up the critical values from the normal (z) or Student’s t (t) distributions, and look up the appropriate critical values. If the conditions are not met, indicate that none of these is applicable: Confidence level Sample size N Population standard deviation Distribution shape Z critical T critical 95% 5 Unknown Normal 95% 10 Unknown Normal 99% 15 Known Skewed 99% 45 Known Skewed 90% 92 Unknown Normal 90% 9 4.2 Skewed 98% 7 27 Normal 98% 37 Unknown Normal

Answer 1

Confidence level	Sample size N	Population standard deviation	Distribution shape	Z critical	T critical	Note
95	5	Unknown	Normal		3.1824	The Critical values are for a two-tailed.
95	10	Unknown	Normal		2.2621	The Critical values are for a two-tailed.
99	15	Known	Skewed			The distribution skewed and hence the conditions are not met.
99	45	Known	Skewed			The distribution skewed and hence the conditions are not met.
90	92	Unknown	Normal		1.6618
90	9	4.2	Skewed			The distribution skewed and hence the conditions are not met.
98	7	27	Normal	2.3263	1.9438	The sample size is 7 and so it appropriate to look at t-table though the population SD is known. The critical value is for a two-tailed distribution
98	37	Unknown	Normal		1.6883	The Critical values are for a two-tailed.