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Mariulka [41]
2 years ago
9

A researcher wants to test if the mean annual salary of all lawyers in a city is different from $110,000. A random sample of 50

lawyers selected from the city reveals a mean annual salary of $ 112000, Assume that σ-$16 100, and that the test is to be made at the 2% significance level What are the critical values of z?
2.33 and 2.33
2.05 and 2.05
-1.645 and 1.645
-1.28 and 1.28
What is the value of the test statistic, z, rounded to three decimal places?
What is the p-value for this hypothesis test, rounded to four decimal places?
Should you reject or fail to reject the null hypothesis in this test?
Mathematics
1 answer:
KiRa [710]2 years ago
5 0

Solution :

This is the two tailed test.

The null hypothesis and the alternate hypothesis is as :

Null hypothesis is $H_0:\mu=110000$

Alternate hypothesis is $H_0:\mu \neq110000$

$\overline x = 112000, \ \mu = 110000, \sigma = 16100, n =  50, \alpha = 0.02$

Therefore, the critical value of z is :

$z_{\alpha} = -2.33 \text{ and}\  2.33$

Now the test statics is :

$z=\frac{\frac{(\overline x - \mu)}{\sigma}}{\sqrt n}$

$z=\frac{\frac{(112000-110000)}{16100}}{\sqrt {50}}$

$z=0.87$

The test statics is 0.878

We see that it is a right tailed test.

$P(z > 0.878)=1-P(z

$P- \text{value}= \ 2 \times 0.19$

              = 0.3800

Thus , P-value > α

So we fail to reject the null hypothesis.

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B. F2. That is the deepest point in the decline.
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3 years ago
Whats 63/100-5/10? with an good 5th grade explanation​
Ilia_Sergeevich [38]

Answer:  .13

Step-by-step explanation:

63/100=0.63

5/10=0.50

=.13

I took 63 and divided it by 100 to get .63 and took 5 and divided it by 10 to get .50 so I took them and subtracted them to get .13

4 0
2 years ago
At Pike Place Fish Market in Seattle, customers can purchase a variety of different types of seafood. One type of seafood sold a
allsm [11]

Answer:

z=1.28

And if we solve for a we got

a=3.6 +1.28*0.8=4.624

So the value of height that separates the bottom 90% of data from the top 10% is 4.624.

So then the best answer for this case would be:

 C. 4.64

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(3.6,0.8)  

Where \mu=3.6 and \sigma=0.8

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.1   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.28

And if we solve for a we got

a=3.6 +1.28*0.8=4.624

So the value of height that separates the bottom 90% of data from the top 10% is 4.624.

So then the best answer for this case would be:

 C. 4.64

8 0
3 years ago
X=8<br> what is the radical equation
kap26 [50]

Answer:

x=64

Step-by-step explanation:

x=8

(x)^2=8^2

x=64

Hope it helps ;)

6 0
3 years ago
Harvey has $390 in a savings account that earns 6% simple interest each year. How much interest will Harvey earn in 2 years, ass
Ganezh [65]

Answer:

Step-by-step explanation:is 6/10

6 0
3 years ago
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