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In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the CDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a mean height of 63.9 inches with a standard deviation of 0.5 inch. Does your sample provide sufficient evidence that women today are taller than in 1990? Perform the appropriate test at the 0.05 level of significance

Respuesta :

Answer:

We reject H₀ , we have enough evidence, women today are taller than in 1990

Step-by-step explanation:

The problem is one tail test. We assume height of women follows normal distribution with σ = 0,5 in.

Then    null hypothesis :      H₀    ⇒   μ₀  =  63.7

    Alternative hipothesis:    Hₐ   ⇒    μ   >  63.7

Significance level   0,05       ⇒  z(c)  = 1.645

Statistic z :

z (c)  = ( μ - μ₀ ) / (0,5/√45)    ⇒  z(c)  = (63.9 - 63.7 ) / (0,5 / √45)

z(c) =( 0,2*  √45 ) / 0,5

z(c) =  2,68

Evaluation :  z(s)  > z(c)      2.68 > 1.645

z(c) is in the rejection area  we reject H₀  

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