A sample of 100 students from a private school produces a mean of 70.30 on a tes

Question

A sample of 100 students from a private school produces a mean of 70.30 on a test of social skills. The national mean for students from public schools is 75.62 (sigma_x = 30.0). We want to discover if private schools perform worse than those in public schools on this measure. What are H_o and H_a for this data? What is z_obt ? With a alpha = .05, what is z_crit ? What should we conclude about this relationship between private schools and social skills-does it represent a new population mean, or not? Describe in words the relationship if there is one. In this example, what is the actual probability of making a Type I error? In this example, what is the probability of making a Type II error?

Explanation / Answer

Ho: mean =75.62 (for private schools)

Ha: mean <75.62

b) std error=std deviation/(n)1/2 =3

hence z obt =(X-mean)/std error =(70.30-75.62)/3 =-1.7733

c)z critical =-1.6449

d)yes it represent a new population mean cause test stat is in rejection region

e)probability of making type I error =0.05

f)probability of making type II error =0.0381

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