"D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours. Because of an improved production process, the company believes that there has been an INCREASE in the life expectancy of its D size batteries. A sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours. Conduct an appropriate hypothesis test. Find the t-statistic and the appropriate conclusion at the 0.1 level of significance.

The calculated value t = 5.608 > 2.3988 at 0.1 level of significance with 53 degrees of freedom.

The null hypothesis is rejected at 0.1 level of significance

The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries

Step-by-step explanation:

Step(i):-

Given data the size of sample n=54

Given "D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours

therefore mean of Population μ = 85.5 hours

Given a sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours

The mean of the sample x⁻ = 88.7 hours

The standard deviation of the sample (S) = 3.8 hours

Step(ii):-

Null hypothesis : H₀:μ > 85.5 hours

Alternative hypothesis: H₁:μ < 85.5 hours

Level of significance : ∝= 0.1

Degrees of freedom γ =n-1 = 54-1 =53

The test statistic

t = 5.608

The tabulated value t = 2.3988 at 0.1 level of significance with 53 degrees of freedom.

Conclusion:-

The calculated value t = 5.608 > 2.3988at 0.1 level of significance with 53 degrees of freedom.

The null hypothesis is rejected at 0.1 level of significance

The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet