A manufacturer of detergent claims that the contents of boxes sold weigh on aver

Question

A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 20 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.5 ounces. A random sample of 16 boxes yielded a sample mean weight of 19.77 ounces. Test at the 10% significance level the null hypothesis that the population mean weight is at least 20 ounces. What are the null and alternative hypotheses for this test? A. H_0: mu lessthanorequalto 20 H_1: mu > 20 B. H_0: mu greaterthanorequalto 20 H_1: mu z_alpha B. Reject H_0 if x bar - mu_0/sigma/square n z_alpha/2 C. Reject H_0 if x bar - mu_0/sigma/square n

Explanation / Answer

(a) Ho : >= 20

Ha : < 20

OPtion b is corrrect.

(b) Here it is one directional test and population standard deviation is given so we shall use Z test.

OPtion C is correct that reject H0 if

(Xbar - 0 ) / ( / sqrt(n)) < - Za

critical value of Z = -Za = 1.28

Test Statistic

(19.77 - 20)/ (0.5/sqrt (16) ) = -0.23/ 0.125 = -1.84

so Z < Za so we can reject the null hypothesis.

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