A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for µd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypothesis below (versus a two-sided alternative) can be rejected?

A. H0: μd= 0.5B. H0: μd= 1.0C. H0: μd= 1.5D. H0: μd= 2.0

Correct option is (A). H₀: = 0.5

Step-by-step explanation:

The (1 - α)% confidence interval for a population parameter can be used to determine whether to reject a null hypothesis or not.

The decision rule is:

If the (1 - α)% confidence interval for a population parameter consists of the null value of the parameter then the null hypothesis will be accepted or else it will be rejected.

A hypothesis test is performed to determine the difference between the ideal and actual heights of college males.

The 95% confidence interval for the mean difference, is:

CI = (0.8, 2.2)

The four null hypothesis provided are:

The 95% confidence interval for the mean difference consists of the value, 1.0, 1.5 and 2.0.

But it does not consist the value 0.5.

So, the null hypothesis that can be rejected is:

H₀: = 0.5

Thus, the correct option is (A).

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,