For a hypothesis test of H0: p = 0.40 against the alternative Ha: p > 0.40, the z test statistic is found to be 2.25. What can be said about this finding? a. The finding is significant at both α = 0.05 and α = 0.01.

b. The finding is significant at α = 0.05 but not at α = 0.01.

c. The finding is significant at α = 0.01 but not at α = 0.05.

d. The finding is not significant at α = 0.05 and α = 0.01.

e. The finding is inconclusive because we don't know the value of p-hat.

B

Step-by-step explanation:

The first thing we need to do here is to find the probability value that corresponds to z-score of 2.25

While this is traceable using the normal distribution table, we can easily find it using the Normal distribution function in excel

By using this, we get the probability P value of the z score 2.25 to be 0.012224

Now, before we can accept or reject H0, we need to compare the value of P to the significance level alpha

If P ≤ alpha, we reject the null hypothesis H0

At alpha = 0.05, p value is lesser , we reject the null hypothesis.

At alpha P 0.01, p value is greater so we accept null hypothesis

This shows that the finding is significant at alpha = 0.05 (since we rejected null hypothesis) but not at alpha = 0.01(since we accepted null hypothesis)

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

x=12 units bd= 10 units

step-by-step explanation: