Chapter 10: Q. 48 (page 598)

Comparing Two Independent Population Proportions.
Use the following information for the next five exercises. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1.
State the null and alternative hypotheses

Short Answer

Expert verified

The null and alternative hypotheses is

$H_{0} : p_{o s 1} = p_{o s 2} H_{1} : p_{o s 1} > p_{o s 2}$

Step by step solution

Given Information

The proportions of system failures for two types of phone operating systems are being compared to see if there is a difference (crashes). Within the first eight hours of operation, fifteen of a random sample of 150 phones with OS1 had system problems. Within the first eight hours of operation, nine out of 150 OS2 phones encountered system problems. OS2 is thought to be more stable than OS1 (it has less crashes).

Determine the null and alternative hypotheses

The null hypothesis states that the proportion of phones with OS1 or OS2 crashes is the same. The alternative hypothesis is that phones running OS2 are more stable than phones running OS1.

By providing null and alternative hypotheses,

$H_{0} : p_{o s 1} = p_{o s 2} H_{1} : p_{o s 1} > p_{o s 2}$