1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marat540 [252]
3 years ago
15

A dataset lists full IQ scores for a random sample of subjects with low lead levels in their blood (sample 1) and another random

sample of subjects with high lead levels in their blood (sample 2). The statistics are summarized below. Use a 0.05 significance level to test the claim that the mean IQ score of people with low blood lead levels is higher than the mean IQ of people with high blood lead levels.
Low Blood Lead Level: n = 78 x = 92.88 s = 15.34
High Blood Lead Level: n = 21 x = 86.90 s = 8.99
a. State and label the null and alternative hypotheses.
b. State the value of the test statistic.
c. Find either the critical value(s) and draw a picture of the critical region(s) or find the P-value for this test. Indicate which method you are using: ( CIRCLE ONE: Critical value / P-value )
Mathematics
1 answer:
Alenkasestr [34]3 years ago
6 0

Answer:

a. Null hypothesis: \mu_1 \leq \mu_2

Alternative hypothesis: \mu_1 >\mu_2

b. t=\frac{(92.88 -86.90)-(0)}{\sqrt{\frac{15.34^2}{78}}+\frac{8.99^2}{21}}=2.282

c. p_v =P(t_{97}>2.287) =0.0122

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Low Blood Lead level) is significantly higher than the mean for the group 2 (High Blood Lead level).  

Step-by-step explanation:

a. State and label the null and alternative hypotheses.

The system of hypothesis on this case are:

Null hypothesis: \mu_1 \leq \mu_2

Alternative hypothesis: \mu_1 >\mu_2

Or equivalently:

Null hypothesis: \mu_1 - \mu_2 \leq 0

Alternative hypothesis: \mu_1 -\mu_2>0

Our notation on this case :

n_1 =78 represent the sample size for group 1

n_2 =21 represent the sample size for group 2

\bar X_1 =92.88 represent the sample mean for the group 1

\bar X_2 =86.90 represent the sample mean for the group 2

s_1=15.34 represent the sample standard deviation for group 1

s_2=8.99 represent the sample standard deviation for group 2

b. State the value of the test statistic.

And the statistic is given by this formula:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{s^2_2}{n_2}}

Where t follows a t distribution with n_1+n_2 -2 degrees of freedom. If we replace the values given we have:

t=\frac{(92.88 -86.90)-(0)}{\sqrt{\frac{15.34^2}{78}}+\frac{8.99^2}{21}}=2.282

Now we can calculate the degrees of freedom given by:

df=78+21-2=97

c. Find either the critical value(s) and draw a picture of the critical region(s) or find the P-value for this test. Indicate which method you are using: ( CIRCLE ONE: Critical value / P-value )

Method used: P value

And now we can calculate the p value using the altenative hypothesis, since it's a right tail test the p value is given by:

p_v =P(t_{97}>2.287) =0.0122

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Low Blood Lead level) is significantly higher than the mean for the group 2 (High Blood Lead level).  

You might be interested in
Helppp pt.5 plzzzzz​
Fiesta28 [93]

Answer: 60 cm²

Step-by-step explanation:

This is pretty simple, we know AB is 12 cm and DE is 4 cm. We know ABC has a total of 180 square centimeters. So...

12 ÷ 3 = 4

180 ÷ 3 = 60

The answer is 60 cm²

I hope this helps!

6 0
3 years ago
Which graph should Laila choose? Explain your reasoning by completing the sentence. Click arrows to choose an answer from each m
Leno4ka [110]

Answer:

box plot

Step-by-step explanation:

6 0
3 years ago
SIMPLIFY THE EXPRESSION (m − 1)(-4)
anastassius [24]

Answer:

-4m + 4

Step-by-step explanation:

you distribute the -4 to the m making -4m and then distribute -4 to the -1 which makes +4

4 0
3 years ago
Help me please cuz some people are senting link when I ask them to not
vladimir2022 [97]

Answer:

the change is 8.4 degrees

Step-by-step explanation:

1.2x7=8.4

3 0
3 years ago
Read 2 more answers
Add 5 1/5 and 4 3/5 as a fraction
kirill115 [55]

Answer:

9 and 4/5

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Multiply. do not round your answer. 9.2 × 14.71
    6·1 answer
  • Solve for x. −4≤11−3x Enter your answer as an inequality in the box.
    14·1 answer
  • Please help and answer
    5·1 answer
  • 2x-1=10 can someone help please?
    9·1 answer
  • a student earns 42 points out of 60 points on a test what percent of the points did the student answer​
    8·2 answers
  • Rewrite 8x8x8 using an exponent
    5·1 answer
  • Ms. Semuskie is buying bagels for her family. How many bagels can she buy for 50$
    13·1 answer
  • Which description best fits the graph?
    14·2 answers
  • Complete the pattern ___ 8,579 ____85.7 8.57____
    10·1 answer
  • After working for 25 hours when water made $375. after working for 40 hours lamar made $600. predict how much he would make up t
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!