Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. the information related to the hypothesis test is presented below. test of h0: f$mu leq f$ 1500 versus h1: f$ mu f$ > 1500 sample mean 1509.5 sample standard deviation 24.27 assuming the life length of this type of lightbulb is normally distributed, what is the p-value associated with this test? place your answer, rounded to 3 decimal places in the blank. for example, .123 would be a legitimate entry.

p score = 0.031

Step-by-step explanation:

We will be running a hypothesis test to find the p-value.  See attached photo for the work needed and the running of the test.

Our hypothesis are:

H0: µ = 1500

HA: µ > 1500 (claim)

They say that the life of the light bulbs are more than 1,500 hours, so that is the alternate hypothesis since it's strictly more than, not equal to or greater.

we have a sample mean of: 1509.5

we have a sample standard deviation of: 24.27

We just need to find the p-value, we don't need to make a conclusion about the test results.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

range is infinite on both x and y axis positive and negative

step-by-step explanation: