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Olenka [21]
3 years ago
14

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of bra

king systems. Use the two-sample t test at significance level 0.01 to test H0: μ1 − μ2 = −10 versus Ha: μ1 − μ2 < −10 for the following data: m = 8, x = 115.6, s1 = 5.04, n = 8, y = 129.3, and s2 = 5.32.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t = ________

P-value = _________
Mathematics
1 answer:
dem82 [27]3 years ago
8 0

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Given that μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems, the hypothesis are

For null,

H0: μ1 − μ2 = - 10

For alternative,

Ha: μ1 − μ2 < - 10

This is a left tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 115.6

x2 = 129.3

s1 = 5.04

s2 = 5.32

n1 = 8

n2 = 8

t = (115.6 - 129.3)/√(5.04²/8 + 5.32²/8)

t = - 2.041

Test statistic = - 2.04

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [5.04²/8 + 5.32²/8]²/[(1/8 - 1)(5.04²/8)² + (1/8 - 1)(5.32²/8)²] = 45.064369/3.22827484

df = 14

We would determine the probability value from the t test calculator. It becomes

p value = 0.030

Since alpha, 0.01 < the p value, 0.03, then we would fail to reject the null hypothesis.

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The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality
egoroff_w [7]

Answer:

1. (a) 32     (b) 8

2. (a) 48.33    (b) 92.75    (c) 9.63

3.  We observe that sample mean of air quality index in Pomona is higher that that of Anaheim which indicates that the level of air pollution is higher in Pomona and there is more health concern here.

On the other hand, the variation in air quality index is higher in Anaheim than in Pomona as Anaheim has higher variance and standard deviation for air quality index which means that there are not much fluctuations in air quality index in Pomona.  

Step-by-step explanation:

First arranging our data of air quality index values for Pomona in ascending order, we get : 28, 42, 45, 48, 49, 50, 55, 58, 60.

  1. (a) Range is given by the formula :

                      Highest value in data - Lowest value in data = 60 - 28 = 32

        (b) Interquartile rage = Third quartile - First quartile

                                           = Q_3 - Q_1

             Q_1 =  (\frac{n-1}{4} )^{th} observation in the data = 2^{nd} obs. { Because n = 9}

                 Therefore, Q_1 = 42.

             Q_3 = (3Q_1)^{th} obs. = (3 x 2 ) = 6^{th} obs = 50

             So, Interquartile rage = 50 - 42 = 8.

     2. (a) Sample mean formula =  \frac{\sum X_i}{n} = \frac{28+ 42+ 45+ 48+ 49+ 50+ 55+ 58+ 60}{9} = 48.33

         (b) Sample variance formula = \frac{\sum (X_i - Xbar)^{2}}{n-1} where Xbar = Sample mean

                                                         = 92.75

          (c) Sample standard deviation  formula = \sqrt{variance} = \sqrt{92.75} = 9.63.

     3. Given that a sample of air quality index readings for Anaheim has   sample mean of 48.3, a sample variance of 136, and a sample standard deviation of 11.66.

We observe that sample mean of air quality index in Pomona is higher that that of Anaheim which indicates that the level of air pollution is higher in Pomona and there is more health concern here.

On the other hand, the variation in air quality index is higher in Anaheim than in Pomona as Anaheim has higher variance and standard deviation for air quality index which means that there are not much fluctuations in air quality index in Pomona.  

                                       

7 0
3 years ago
Change the following algebraic expressions to the statement in words: i. 3mn +7 ii. xy + (x+y)
kicyunya [14]

Answer:

i) 3*m*n + 7

Then we can write the first term as:

"3 times the product between two numbers"

Where the product of two numbers is m*n

And after that we need to add 7, then the complete sentence is:

"3 times the product between two numbers, increased by 7"

ii) x*y + (x + y)

The first part, x*y, can be written as:

"the product of two numbers"

where the two numbers are the number x and the number y.

After that, we add the sum of these two numbers, then the complete sentence can be:

"the product of two numbers, plus the sum of these two numbers"

8 0
3 years ago
You go to the store and pick out 3 apples for $0.60 each, 2 bananas for $0.50 each, and 1 quart of yogurt for $4.50. At checkout
Arlecino [84]

Answer:

$5.44

Step-by-step explanation:

3 0
3 years ago
Darryl is considering a purchase of a $125,000 home at 6.5%. Under this rate,
raketka [301]

Answer:

122 months or just over 10 years

Step-by-step explanation:

3 0
3 years ago
Anton bought a picnic cooler. His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cool
Rus_ich [418]
7.95 ÷ 1.06 = $7.50

This works as by dividing 7.95 by the percentage multiplier 1.06 it will give you the original amount.

An alternative method is to find out what 100% (7.95) is, then divide by 10 to find 10% and then divide by 10 again to find 1% and then multiply the 1% by 6 and subtracting the answer from 7.95.
7 0
3 years ago
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