Question

Oven thermostats were tested by setting them to 350oF and measuring the actual
temperature of the oven. In a sample of 67 thermostats, the average temperature
was 348.2oF. If the standard deviation of the population is known to be σ = 5.1oF
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 ±0.8oF?

Answer 1

Solution :

(i)

Z_$\alpha$/2 = 1.96

Margin of error = E = Z_$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 1.96 * (5.1 / $\sqrt$ 67)

= 1.2

At 95% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

348.2 - 1.2 < $\mu$ < 348.2 + 1.2

347.0 < $\mu$ < 349.4

(347.0 , 349.4)

(ii)

Z_$\alpha$/2 = 1.96

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [1.96 * 5.1 / 0.8]²

n = 157

157 thermostats must be sampled .