Question

NASA has been working with utility companies to set up expensive power generating windmills. In order for a site to be effective, the average wind speed must be more than 20 mph. At a specific site, NASA took a sample of forty-five wind speed readings. The sample average wind speed is 21.7 mph with a standard deviation of 4.2 mph. NASA will only build the windmill if they are sure that the true average wind speed is greater than 20 mph.

a. Should they build the windmill? Justify by conducting a hypothesis test at α = 0.05.

b. Describe in the words of the problem what making a Type I error would be and its likely consequences

c. Describe in the words of the problem what making a Type II error would be and its likely consequences.

Answer 1

Answer:

1 a)

Given

sample n = 45

xbar = 21.7 mph

Standard deviation = 4.2 mph

mean u = 20 mph

we need to test

Ho : xbar = u

Ha : xbar > u

let us consider,

test statistic t = (x-u)/(s/sqrt(n))

substitute values

t = (21.7 - 20)/(4.2/sqrt(45))

t = 2.72

degree of freedom = n - 1 = 45 - 1 = 44

The p-esteem for above test is 0.0047 [since from t table]

P value = 0.0047

The acquired p-esteem is < 0.05

i.e.,

which recommends that we have solid proof against Ho yo dismiss it and we can presume that example normal breeze speed is in excess of 20 mph and furthermore we can counsel that they should constructed the windmill.

1b)

The sort I error is characterized as dismissing Ho when it is valid.

In this issue if genuine windspeed isn't more prominent than 20 mph and still we dismiss the invalid theory based on test confirms then we are making a sort I error and it will influence the force age of windmills.

By submitting type-I mistake we are wrongly setting up the force producing windmills at the site and in the event that the windmills are not more prominent than 20 mph, at that point the windmills won't be viable.

1c)

The sort II error is characterized as tolerating Ho when it is bogus.

In this issue, if the real wind speed is more noteworthy than 20 mph and we acknowledge the invalid theory that the breeze speed isn't more prominent than 20 mph based on test confirms then we are making a sort II mistake.

By submitting a sort II mistake, we won't propose to manufacture a force creating windmill on the site while it is appropriate to construct a force producing windmill on the site.