The methods for proportions discussed in Section 4.3 assume that np0 5 and n( 1 - p0) 5. When sample sizes are smaller, then methods based directly on the binomial distribution can be used. Suppose...

The methods for proportions discussed in Section 4.3 assume that np₀

5 and n( 1 - p₀)

5. When sample sizes are smaller, then methods based directly on the binomial distribution can be used. Suppose a vendor claims that at most 5% of parts are defective. In a random sample of 20 parts shipped by this vendor, you find four that are defective.

(a) State the null and alternative hypotheses.

(b) Show that this sample size is too small for the z test for proportions.

(c) Calculate the p value for this test, using the binomial distribution with

p = 0: 05.

(d) What do you conclude, if you are using α = 0:05?