An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for 90 days in each region. The mean wind speed in Region A is 13.9 miles per hour. Assume the population standard deviation is 2.9 miles per hour. The mean wind speed in Region B is 15.1 miles per hour. Assume the population standard deviation is 3.3 miles per hour. At alphaequals0.05, can the company support the researcher's claim? Complete parts (a) through (d) below.

We conclude that the wind speed in Region A is less than the wind speed in Region B which means researcher's claim was correct.

Step-by-step explanation:

We are given that a researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for 90 days in each region.

The mean wind speed in Region A is 13.9 miles per hour. Assume the population standard deviation is 2.9 miles per hour. The mean wind speed in Region B is 15.1 miles per hour. Assume the population standard deviation is 3.3 miles per hour.

Let = mean wind speed in Region A.

= mean wind speed in Region B.

SO, Null Hypothesis, :      {means that the wind speed in Region A is more than or equal to the wind speed in Region B}

Alternate Hypothesis, :      {means that the wind speed in Region A is less than the wind speed in Region B}

The test statistics that would be used here Two-sample z-test statistics as we know about population standard deviations;

                              T.S. =    ~ N(0,1)

where, = sample mean wind speed in Region A = 13.9 miles per hour

= sample mean wind speed in Region B = 15.1 miles per hour

= population standard deviation in Region A = 2.9 miles per hour

= population standard deviation in Region B = 3.3 miles per hour

= sample of days speed calculated in Region A = 90

= sample of days speed calculated in Region A = 90

So, the test statistics  =  

                                     =  -2.591

The value of z test statistics is -2.591.

Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

Since our test statistic is less than the critical value of z as -2.591 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the wind speed in Region A is less than the wind speed in Region B which means researcher's claim was correct.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3