Question

Using Technology. In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use $\alpha$= 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

c. What is the P-value?

d. What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

Cell Phone Ownership A Pew Research Center poll of 2076 randomly selected adults showed that 91% of them own cell phones. The following Minitab display results from a test of the claim that 92% of adults own cell phones.

Short answer

a. The test is two-tailed.

b. The value of the test statistic (z-score) is equal to -1.69.

c. The p-value is equal to 0.091.

d. The null hypothesis is that the proportion of adults who own cell phones is equal to 0.92.The decision is fail to reject the null hypothesis.

e. There is not enough evidence to warrant rejection of the claim that the proportion of adults who own cell phones is equal to 92%.

Step-by-step solution

Given information

It is given that in a survey, out of 2076 adults, 92% of them own cell phones.

Tail of the Test

a.

According to the given claim, the proportion of adults who own cell phones is equal to 92%.

The null hypothesis is represented as follows:

$H_0:p=0.92$

The alternative hypothesis is represented as follows:

$H_1:p\ne 0.92$

Since there is an unequal sign in the alternative hypothesis, the test is two-tailed.

Test Statistic

b.

The test statistic to test the given claim is the z-score.

Here, the value of the test statistic (z-score) is equal to -1.69.

P-Value

c.

The p-value corresponding to the z-score of -1.69 is given to be equal to 0.091.

Null hypothesis and its conclusion

d.

The null hypothesis for this test is as follows:

Null Hypothesis: The proportion of adults who own cell phones is equal to 92%.

Symbolically, $H_0:p=0.92$where

p is the proportion of adults who own cell phones.

Here, the p-value equal to 0.091 is greater than the significance level of 0.05. Thus, the null hypothesis fails to be rejected.

Conclusion of the Test

e.

There is not enough evidence to warrant rejection of the claim that the proportion of adults who own cell phones is equal to 92%.