Suppose that the mean height of women age 20 years or older in a certain country

Question

Suppose that the mean height of women age 20 years or older in a certain country is 62.5 inches. One hundred randomly selected women in a certain city had a mean height of 61.7 inches. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean height of women in the city differs from the national mean? Assume the population standard deviation of heights of women in the country is 3.8 inches.

a. Hypotheses: ??0:____________________________ ????: _______________________________________

b. Compute the test statistic, Round to two decimal places.

c. Sketch the curve needed for this problem and label it either ?? or ?? as appropriate. Shade in the area for this problem. Determine the ??-value.

d. Should the null hypothesis be rejected?

e. Interpret your result in the context of the problem in a sentence

Explanation / Answer

Ho = mean height city = mean height country

h1 mean height city and for country are different

t= (m1-m2)/sd/sqrt(n)

(61.7-62.5) /3.8/sqrt(100)

=-2.105263

z critical at 10% significance 1.646

c)

we ca use . z test as sample size >30

d) as |t| > t critical at 10% we cn reject the null

the average height of the city is different from the country

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