Amanufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. someone in the research and development division of the shoe company claims to have developed a longer lasting product. this new product was worn by 30 individuals and lasted on average for 17 months. the variability of the original shoe is estimated based on the standard deviation of the new group which is 5.5 months. is the designer's claim of a better shoe supported by the trial results? base your decision on a two tailed testing using a level of significance of p < .05.

Step-by-step explanation:

Hello!

So you have a new type of shoe that lasts presumably longer than the ones that are on the market. So your study variable is:

X: "Lifetime of one shoe pair of the new model"

Applying CLT:

X[bar]≈N(μ;σ²/n)

Known values:

n= 30 shoe pairs

x[bar]: 17 months

S= 5.5 months

Since you have to prove whether the new shoes last more or less than the old ones your statistical hypothesis are:

H₀:μ=15

H₁:μ≠15

The significance level for the test is given: α: 0.05

Your critical region will be two-tailed:

So you'll reject the null Hypothesis if your calculated value is ≤-1.96 or if it is ≥1.96

Now you calculate your observed Z-value

Z=x[bar]-μ ⇒ Z=    17-15     = 1.99

     σ/√n              5.5/√30

Since this value is greater than the right critical value, i.e. Zobs(1.99)>1.96 you reject the null Hypothesis. So the average durability of the new shoe model is different than 15 months.

I hope you have a SUPER day!

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

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation: