Question

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.

a. Is this a test of means or proportions?

b. What is the random variable?

c. State the null and alternative hypotheses.

d. What is the p-value?

e. What can you conclude about the two operating systems?

Answer 1

(a)

Question:

Is this a test of means or proportions?

This is a test of proportions.

(b)

Question:

What is the random variable?

The random variable is system failures (crashes)

(c)

Question:

State the null and alternative hypotheses

Answer:
H0: Null Hypothesis: p1 = p2 ( There is no difference in the proportions of system failures (crashes) )

HA: Alternative Hypothesis: p1 p2 ( There is a difference in the proportions of system failures (crashes) ) (Claim)

(d)

n1 = 150

1 = 15/150 = 0.1

n2 = 150

2 = 9/150 = 0.06

Pooled Proportion is given by:

Test Statistic is given by:

By Technology, P- Value = 0.2016

So,

the p-value = 0.2016

(e)

Since P - Value = 0.2016 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that there is a difference in the proportions of system failures (crashes).