Question

the following data represent the projection times of the films produced by two cinematographic companies.

Company 1	102	86	98	109	87	100
Company 2	81	165	97	134	87	114

Find a confidence interval for the average projection time differences of the films produced by company 1 and company 2. Use a significance level of 0.10 and assume that the distribution is normal.

Answer 1

							Average	Std. Dev
Company 1	102	86	98	109	87	100	97	8.944272
Company 2	81	165	97	134	87	114	113	31.9437

here

we have to find the confidence interval for  the average projection time differences of the films produced by company 1 and company 2

here degree of freedom = 6

= + - t_critical sqrt [s₁²/n₁ + s₂²/n₂]

= (97 - 113) +- 1.9432 * sqrt [8.9443²/6 + 31.9437²/6]

= -16 +- 1.9432 * 13.5425

= (-42.3156, 10.3156)

so here as the confidence interval consists value of zero so we say that there is no significant average projection time differences of the films produced by company 1 and company 2