An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and T test statistic. (a) HA: μ > 0.5, n = 21, T = 2.485 p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 Determine if the null hypothesis would be rejected at α = 0.01. reject H0 fail to reject H0 Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) HA: μ < 3, n = 17, T = 0.5 p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 Determine if the null hypothesis would be rejected at α = 0.01.

(a) The correct interval is, 0.010 < p-value < 0.025. Fail to reject H₀.

(b) The correct interval is, p-value > 0.100. Fail to reject H₀.

Step-by-step explanation:

(a)

The information provided is:

Hₐ: μ > 0.5, n = 21, t = 2.485

Compute the p-value as follows:

The correct interval is, 0.010 < p-value < 0.025.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.011 > α = 0.01

Fail to reject H₀.

(b)

The information provided is:

Hₐ: μ < 3, n = 17, t = 0.5

Compute the p-value as follows:

The correct interval is, p-value > 0.100.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.312 > α = 0.01

Fail to reject H₀.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

77

step-by-step explanation: