The diameter of a spindle in a small motor is supposed to be 5 mm. if the spindle is either too small or too large, the motor will not work properly. the manufacturer measures the diameter in a sample of motors to determine whether the mean diameter has moved away from the target. what are the null and alternative hypotheses (h0 = null hypothesis and ha = alternative hypothesis)?

(a) h0: mean= 5 and ha: mean is not equal to 5
(b) h0: mean = 5 and ha: mean < 5
(c) h0: mean < 5 and ha: mean > 5
(d) h0: mean = 5 and ha: mean > 5

a) H0: mean =5 and Ha: mean≠ 5

Step-by-step explanation:

In hypothesis testing procedure the trait of null hypothesis is that it always contain an equality sign. We are known that diameter of spindle is known to be 5mm. This our null value. Hence the null hypothesis is

H0:μ=5.

Now for alternative hypothesis we are given that the mean diameter has moved away from the target. This means that mean diameter could be increases or decreases from 5mm. Hence the alternative hypothesis is

Ha:μ≠5

range =5

step-by-step explanation:

to find the range, we take the largest value and subtract the smallest value.

the largest value is 5

the smallest value is 0

the range is 5-0   =5

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west