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Mathematics

1 answer:

Elina [12.6K]3 years ago

6 0

Answer:

How do I answer theese quistions? do I message you or...

Step-by-step explanation:

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Use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothe

omeli [17]

Answer:

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Step-by-step explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.

If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.

(a) Now, we are given alternate hypothesis, $H_1$ : p < 3/5

Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

P-value = P(Z < -1.68) = 1 - P(Z $\leq$ 1.68)

= 1 - 0.95352 = 0.0465

Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which we reject the null hypothesis.

(b) Now, we are given alternate hypothesis, $H_1$ : p > 0.383

Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

P-value = P(Z > 0.41) = 1 - P(Z $\leq$ 0.41)

= 1 - 0.6591 = 0.3409

Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject the null hypothesis.

5 0

3 years ago

The product of two integers is eighty,their quotient is five.Write both integers in numerical order and separated by a comma,no

Goryan [66]

SOLUTION

Let the two integers be x and y.

Now, the product of x and y, is 80, that is

$\begin{gathered} x\times y=80 \\ xy=80\ldots\ldots\text{.equation 1} \end{gathered}$

The quotient of x and y is 5, that is

$\begin{gathered} x\div y=5 \\ \frac{x}{y}=5\ldots\ldots\ldots\ldots\text{.}\mathrm{}\text{equation 2} \end{gathered}$

From equation 2, make x, the subject, we have

$\begin{gathered} \frac{x}{y}=5 \\ \text{cross multiplying } \\ 5\times y=x \\ x=5y \end{gathered}$

Now substitute the x for 5y into equation 1, we have

$\begin{gathered} xy=80 \\ 5y\times y=80 \\ 5y^2=80 \\ \text{dividing by 5} \\ y^2=\frac{80}{5} \\ y^2=16 \\ \text{take square root of both sides } \\ \sqrt[]{y^2}=\sqrt[]{16} \\ \text{square cancels root} \\ y=4 \end{gathered}$

Now substitute y for 4 into any of the equations.

Let us use equation 1 again, we have