Which graph best represents the solution to the following pair of equations?

According to the US Bureau of labor statistics, 7% of US female workers between 16 and 24 years old are paid at the minimum wage

vladimir1956 [14]

Answer:

The Null Hypothesis is $H_o:k_o = 0.07$

The alternative hypothesis is $H_a :k_o \ne 0.07$

Decision rule

If the test staistics is greater than the critical value of significance level then $H_o$ is accepted else $H_o$ is rejected

With the above in mind

The critical value of the significance level which is obtained from the table is

$t_{0.05} = 1.645$

Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected

Conclusion

The information is not enough to back the claim that state differs from the nation

Step-by-step explanation:

From the question we are told that

The percentage of US female workers paid at the minimum wage or less is $k_o =$ 7% = 0.07

The sample size is $n = 500$

The number paid minimum wage or less is x = 42

The significance level is $\alpha =$ 5% = 0.05

Now the probability of getting a US female workers paid at the minimum wage or less is mathematically represented as

$\= k = \frac{x}{n}$

substituting value

$\= k = \frac{42}{500}$

$\= k = 0.084$

The Null Hypothesis is $H_o:k_o = 0.07$

The alternative hypothesis is $H_a :k_o \ne 0.07$

Generally the test statistics is mathematically evaluated as

$z = \frac{\= k - k_o}{\sqrt{\frac{k_o(1-k_o)}{n} } }$

substituting value

$z = \frac{0.084 - 0.07}{\sqrt{\frac{0.07 (1-0.07)}{500} } }$

$z = 1.23$

Now the Decision rule is stated as

If the test staistics is greater than the critical value of significance level then $H_o$ is accepted else $H_o$ is rejected

With the above in mind

The critical value of the significance level which is obtained from the table is

$t_{0.05} = 1.645$

Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected

So the conclusion will be

The information is not enough to back the claim that state differs from the nation

4 0

3 years ago

An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive pr

LenKa [72]

Answer:

(a) The correct option is: H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b) Explained below.

(c) The better value of α will be 0.10.

Step-by-step explanation:

An automobile manufacturer is considering using robots for part of its assembly process only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers.

To test whether the proportion of defective installations is less for the robots than for human assemblers use a single-proportion z-test.

(a)

The hypothesis can be defined as:

H₀: The proportion of defective installations is same for both the robots and human assemblers, i.e. p = 0.02.

Hₐ: The proportion of defective installations is less for the robots than for human assemblers, i.e. p < 0.02.

The alternate hypothesis is the claim or the statement that is being tested.

In this case we need to test whether the proportion of defective installations is less for the robots than for human assemblers or not, so that the manufacturer can decide whether they want to apply the conversion.

Thus, the correct option is:

H₀: p = 0.02 vs. Hₐ: p < 0.02.

(b)

A type I error occurs when we discard a true null hypothesis and a type II error is made when we fail to discard a false null hypothesis.

In this case a type I error will be committed if conclude that the proportion of defective installations is less for the robots than for human assemblers when in fact it is not.

And a type II error will be committed if we fail to conclude that proportion of defective installations is less for the robots than for human assemblers.

(c)

The power of the test is the probability of rejecting a false null hypothesis.

The power of the test sis affected by the significance level of the test (α).

Lesser the significance level of the test the lesser is the power of the test.

If the value of α is reduced from 0.05 to 0.01 then the region of acceptance will increase. This implies that there is low probability of rejecting the null hypothesis even when it is false.

So higher the value of α the higher is the probability of making a correct decision.

Thus, the better value of α will be 0.10.

3 0

3 years ago

Solve the inequality 2ax-3<4x+5a for all possible values of the parameter a

olga_2 [115]

Answer:

Step-by-step explanation:

2ax−3<4x+5a

Step 1: Add -5a to both sides.

2ax−3+−5a<5a+4x+−5a

2ax−5a−3<4x

Step 2: Add 3 to both sides.

2ax−5a−3+3<4x+3

2ax−5a<4x+3

5 0

3 years ago

What percentage of the audience from the 16-25 age group gave the movie a poor rating? 6.19% 10.00% 25.34% 15.70% 16.22%

just olya [345]

We have to find what percent of the audience from the 16-25 age group gave the movie poor rating. There were 113 viewers from this group. There were 7 of them that gave the movie poor rating. We will use the proportion: 113 / 7 = 100% / x% . Then we will cross multiply: 113 x = 700; x = 700 : 113; x = 6.19%. Answer: A ) 6.19%.

7 0

3 years ago

Read 2 more answers

Is the number 282.5 the same as 282.50?

tatyana61 [14]

Yes because the zero has no value.

4 0

3 years ago

Read 2 more answers