Question

The manager of Tea for Us has been ordering stock based on the assumption that 51% of her customers prefer black teas. The following hypotheses are given:

H₀: p = 0.51

H₁: p ≠ 0.51

She sampled 158 of her customers and found that only 41% of those preferred black teas. At the 0.10 significance level, can the null hypothesis be rejected?

a. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)

(Click to select)  Reject  Not reject  H₀  (Click to select)  and reject  and accept  H₁ if z >  or z <  .

b. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round your answer to 2 decimal places.)

Value of the test statistic            

c. What is your decision regarding the null hypothesis?

The null hypothesis is  (Click to select)  Not rejected  Rejected  .

Answer 1

Solution :

a )This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.51

Ha : p 0.51

n = 158

= 0.41

P0 = 0.51

1 - P0 = 1 - 0.51 =0.49

b )Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.41 -0.51 / [(0.51*0.49) / 158 ]

= -2.51

Test statistic = z = -2.51

P(z < -2.51) = 0.0060

P-value = 2 *0.0060 =0.0120

= 0.10

P-value <

0.0120 < 0.10

c ) Reject the null hypothesis .

There is sufficient evidence to suggest that