# View the step-by-step solution to: A survey of 100 mayonnaise purchasers showed that 65 were loyal

A survey of 100 mayonnaise purchasers showed that 65 were loyal to one brand. For 100 bath soap purchasers, only 53 were loyal to one brand. Let p1 = the proportion of loyal mayonnaise purchasers, and p2 = proportion of loyal soap purchasers.
Choose the appropriate hypothesis and decision rule at a = .05.

H0: π1 = π2 versus H1: π1 ≠ π2. Reject the null hypothesis if z < -1.96 or z > 1.96.
H0: π1 = π2 versus H1: π1 ≠ π2. Reject the null hypothesis if -1.96 < z < 1.96.
H0: π1 ≠ π2 versus H1: π1 = π2. Reject the null hypothesis if z < -1.96 or z > 1.96.
H0: π1 ≠ π2 versus H1: π1 = π2. Reject the null hypothesis if -1.96 < z < 1.96.

(b)
Calculate z

(c)
Can we reject the null hypothesis?

Yes
No

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