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
Simplify. 8u+9v+3u−5v
musickatia [10]
Combine like terms
8u+3u= 11u
and
9v-5v= 4v
So the answer is 11u+4v
8 0
3 years ago
Create an equation that matches this table
Radda [10]

The equation that matches the given table is

y = 10x + 40

Solution:

General equation of a line : y = mx + c

Let us find the equation of the table.

<u>Common differences of X: </u>

0 – 1 = 1, 1 – 2 = 1, 3 – 2 = 1, 4 – 3 = 1, 5 – 4 = 1

<u>Common differences of Y: </u>

50 – 40 = 10, 60 – 50 = 10, 70 – 60 = 10, 80 – 70 = 10, 90 – 80 = 10

$m=\frac{\Delta y}{\Delta x}

$m=\frac{10}{1}

m = 10

Substitute m = 10 in general equation of a line

y = 10x + c

To find the constant term, substitute x = 0 and y = 40.

40 = 10(0) + c

40 = 0 + c

40 = c

c = 40

Therefore the equation of a line is y = 10x + 40.

Hence the equation that matches the given table is y = 10x + 40.

6 0
2 years ago
Help need it asap plessss
Dennis_Churaev [7]

Answer:

C) $14.2

Step-by-step explanation:

$3 is flat value. minimum price. $0.8 per mile for 14 miles is 0.8x14 which equals to 11.2. Add $3 and get $14.2.

7 0
2 years ago
Read 2 more answers
Guys I need help in both please​
IRINA_888 [86]

Answer:

Graph 1 is not proportional

Graph 2 is proportional - y is 2 times x

Step-by-step explanation:

In graph 1, there is no x-y correlation

In graph 2, there is, when x=1, y=6

when x=2, y=12. Therefore, when x=3 y would equal 18.

4 0
3 years ago
sheila mixed 3 oz of blue paint wih 2 oz of yellow paint she decided to create 20 oz of he same mixture how many oz of yello pai
FrozenT [24]
I believe it would be 8oz of yellow
8 0
3 years ago
Read 2 more answers
Other questions:
  • Anil wants to multiply 5, 6, and 3. Which expression could Anil write in the box to
    7·2 answers
  • Which is equivalent 4 pencils for every 2 student
    8·2 answers
  • Write the number in standard form.<br><br> 7×10^7
    5·2 answers
  • Solve the equation
    10·1 answer
  • If DA equals 6 units, AB equals 16 units, and HE equals 36 units, what does EF equal?​
    14·1 answer
  • A round Barbecue Pit is 2 meters in diameter what is the distance around the barbecue pit
    13·1 answer
  • Three times the greater of two consecutive odd integers is five less than four
    14·1 answer
  • 3x+5=17 what's the answer
    10·2 answers
  • Margo can purchase tile at a store for $0.69 per tile and rent a tile saw for $36. At another store she can borrow the tile saw
    11·2 answers
  • Solve for x in the triangle. Round your answer to the nearest tenth.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!