A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 732 hours. A random sample of 28 light bulbs has a mean life of 704 hours. Assume the population is normally distributed and the population standard deviation is 65 hours. At alphaequals0.05, do you have enough evidence to reject the manufacturer's claim?

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≥ 732

For the alternative hypothesis,

µ < 732

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = lifetime of the bulb

µ = mean lifetime

σ = standard deviation

n = number of samples

From the information given,

µ = 732

x = 704 hours

σ = 65 hours

n = 28

z = (704 - 732)/(65/√28) = - 2.28

Looking at the normal distribution table, the probability corresponding to the z score is 0.011

Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is enough evidence to reject the manufacturer's claim

Step-by-step explanation:

(-6,-5) , ( 0,-1)  , (-3 , -3) , (2 , 0 ) are solution of the inequalities.

The point that lies on the purple area and on the solid line are the solutions of the equations.