Question

2. Oven thermostats were tested by setting them to 350°F and measuring the actual temperature of the oven. In a sample of 67 thermostats, the average temperature was 348.2°F. If the standard deviation of the population is known to be o = 5.1°F do the following: (i) Find a two-sided 95% confidence interval for the mean oven temperature. (ii) How many thermostats must be sampled so that the 90% confidence interval specifies the mean within +0.8°F?

Answer 1

solution- Given dato 067 348-27 =5.1°F (1) Here we find the asy. ob confidence interval for Mean oven Herperature, fostelo! q C-I = ñ 2 Here! <= 1-0.95 t = 0.05 [asv.] 2 2 2 = 2005 -1.96 r food norral Lastribution teille I 348.2 96.5 = 348-2 £1.96 (ta) = 348.2 $ 1.96(0.6.231) - 34812 & 1.22 348.2 -- 122, 348.2 +1-22 954.49€• I- (346.98, 349.43]

the 954. ob confidence interval tod the reano tenperature is 346.98, 349.42 Here we find the the nostats na? Given! tovaralo 4.3 La 1-0.90 [201.] t = 2 o 1.645 f from noftral l distribution table] => na eu in = [(isus) ) n= [(1-6u5)( 6:325))?