• A researcher claims that less than 40% of U.S. cell phone owners use their phone for most of their online browsing. In a random sample of 100 adults, 31% say they use their phone for most of their online browsing. At 1% level of significance, is there enough evidence to support the researcher’s claim?

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.

Step-by-step explanation:

Set up hypotheses:

Null hypotheses = H₀: p = 0.40

Alternate hypotheses = H₁: p < 0.40

Determine the level of significance and Z-score:

Given level of significance = 1% = 0.01

Since it is a lower tailed test,

Z-score = -2.33 (lower tailed)

Determine type of test:

Since the alternate hypothesis states that less than 40% of U.S. cell phone owners use their phone for most of their online browsing, therefore we will use a lower tailed test.

Select the test statistic:

Since the sample size is quite large (n > 30) therefore, we will use Z-distribution.

Set up decision rule:

Since it is a lower tailed test, using a Z statistic at a significance level of 1%

We Reject H₀ if Z < -1.645

We Reject H₀ if p ≤ α

Compute the test statistic:

[tex]$ Z = \frac{\hat{p} - p}{ \sqrt{\frac{p(1-p)}{n} }} $[/tex]

[tex]$ Z = \frac{0.31 - 0.40}{ \sqrt{\frac{0.40(1-0.40)}{100} }} $[/tex]

[tex]$ Z = \frac{- 0.09}{ 0.048989 } $[/tex]

[tex]Z = - 1.84[/tex]

From the z-table, the p-value corresponding to the test statistic -1.84 is

p = 0.03288

Conclusion:

We failed to reject H₀

Z > -1.645

-1.84 > -1.645

We failed to reject H₀

p > α

0.03 > 0.01

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.