5.51 Apps not working on smartphone. In a survey titled U.S. Smartphone Use in 2

Question

5.51 Apps not working on smartphone. In a survey titled U.S. Smartphone Use in 2015, 90% of smartphone users indi- cated that they have had a problem with a downloaded application (app) on their cell phone not working cor- rectly. Assume this percentage applies to all smartphone users in the United States. In a random sample of 75 smartphone users, suppose that fewer than 60 indicate that they have had a problem with an app on their cell phone not working correctly. What inference can you make about the true proportion of smartphone users who have a problei with apps not working on their cell phone? p.90; normal approx. not valid

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.90
Alternative hypothesis: P < 0.90

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.03464
z = (p - P) /

z = - 2.89

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than -2.89.  

Thus, the P-value = 0.0019.

Interpret results. Since the P-value (0.0019) is less than the significance level (0.05), we cannot accept the null hypothesis.

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