Question

An electrical rm manufactures light bulbs that have a life span that is approximately normally distributed. The population standard deviation is not known. A sample of 30 bulbs are found to have an average life span of 800 hours and a sample standard deviation of 45 hours. Test the hypothesis that µ = 800 against the alternative µ ≠ 800 if a random sample of 30 bulbs has an average life 788 hours. Use P value in your answer.

Answer 1

Answer:

The 't' test statistic = 1.46 < 1.69

The test of hypothesis is H 0 :μ = 800 is accepted

A sample of 30 bulbs are found came from average µ= 800

Step-by-step explanation:

Step 1:-

Given population of mean μ = 800

given size of small sample n =30

sample standard deviation 'S' = 45

Mean value of the sample χ = 788

Null hypothesis $H_{0} =$µ  =800

alternative hypothesis  $H_{1} =$ µ ≠ 800

Step 2:-

The 't' test statistic t =  $\frac{x-μ}{\frac{sig}{\sqrt{n} } }$

                             $t = \frac{788-800}{\frac{45}{\sqrt{30} } }$

                       t = $\frac{12}{8.215}$ = 1.4607

Step 3:-

The degrees of freedom γ = n-1 = 30-1 =29

From "t" value from table at 0.05 level of significance ( t = 1.69)

The calculated value t = 1.4607 < 1.69

Therefore The null hypothesis H_{0} ' is accepted.

conclusion:-

A sample of 30 bulbs are came found from average µ= 800