Refer to Exercise 8.

a. Find a 99% upper confidence bound for the mean temperature.

b. The claim is made that the mean temperature is less than 349.5°F. With what level of confidence can this statement be made?

Exercise 8

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 and the standard deviation was 5.1°F.

a. Find a 90% confidence interval for the mean oven temperature.

b. Find a 95% confidence interval for the mean oven temperature.

c. What is the confidence level of the interval (347.5, 348.9)?

d. How many thermostats must be sampled so that a 90% confidence interval specifies the mean to within ±0.8°F?

e. How many thermostats must be sampled so that a 95% confidence interval specifies the mean to within ±0.8°F?

Solution 15E

Step1 of 3:

Let us consider a random variable X it represents the oven temperature. Here random variable X follows normal distribution with mean standard deviation and n = 67.

That is

The probability density function of normal distribution is given by

, .

Where,

x = random variable

= mean of X

= variance of X

= standard deviation os X

= mathematical constant and its value is 3.14

Here our goal is:

a). We need to find a 99% upper confidence bound for the mean temperature.

b). We need to find level of confidence can this statement be made by taking the mean temperature is less than 349.5°F.

Step2 of 3:

a).

Here we have to find 99% CI, let us take .

Now,

= 0.01

Z-scores(are to the right) is given by

is...