Dullco manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable cd player. but tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. in a left-tailed test at α = .05, which is the most accurate statement?

we would strongly reject the claim.

we would clearly fail to reject the claim.

we would face a rather close decision.

we would switch to α = .01 for a more powerful test.

We would face a rather close decision and switch to α = .01 for a more powerful test.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 40 hours

Sample mean, = 37.8 hours

Sample size, n = 108

Alpha, α = 0.05

Sample standard deviation, s = 5.4 hours

First, we design the null and the alternate hypothesis

We use one-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,                    

We fail to reject the null hypothesis and accept the null hypothesis. Thus, we conclude that alkaline batteries last at least 40 hours on average in a certain type of portable CD player.

But we faced a close decision. By decreasing alpha we could get stronger results. We would switch to α = .01 for a more powerful test.

  6 +2√3 ft²

Step-by-step explanation:

Given a triangular pyramid with ...

Find

Solution

Since corresponding edges are the same length, the area of each of the three faces is (6 ft²)/3 = 2 ft². This can be computed by ...

  A = (1/2)s²·sin(α)

where s is the lateral edge length and α is the angle at the apex formed by the two edges that meet there. Filling in the given values, we find ...

  2 ft² = (1/2)(2 ft)²·sin(α)

  1 = sin(α)   ⇒   α = 90°

That is, each face of the pyramid is an isosceles right triangle with legs of length 2 ft. The hypotenuse of that triangle, the base edge of the pyramid, is then 2√2 ft.

So, the base is an equilateral triangle with edge lengths 2√2 ft. Its area can be computed from ...

  A = (√3)/4·s²

where s is the edge length of the equilateral triangle. That is, the base area is ...

  A = (√3)/4·(2√2)² = 2√3 . . . . square feet

So, the total surface area of the pyramid is ...

  (6 +2√3) ft² ≈ 9.4641 ft² . . . . . total surface area