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?

Self-Driving Vehicles In a TE Connectivity survey of 1000 adults, 29% said that they would feel comfortable in a self-driving vehicle. The accompanying StatCrunch display results from testing the claim that more than 1/4 of adults feel comfortable in a self-driving vehicle.

Short answer

a. The test is right-tailed.

b. The value of the test statistic (z-score) is equal to 2.9212.

c. The p-value is equal to 0.0017.

d. The null hypothesis is that the proportion of adults who would feel comfortable in a self-driving vehicle is equal to 25% or 0.25.The null hypothesis is rejected.

e. There is enough evidence to conclude that the proportion of adults who would feel comfortable in a self-driving vehicle is greater than 0.25.

Step-by-step solution

Given information

It is given that out of 1000 adults, 29% of them would feel comfortable in a self-driving vehicle.

Tail of the test

a.

According to the given claim, the proportion of adults who would feel comfortable in a self-driving vehicle is more than $\frac{1}{4}$ or 0.25.

The null hypothesis is represented as follows:

$H_0:p=0.25$

The alternative hypothesis is represented as follows:

$H_1:p>0.25$

Since there is a greater than sign in the given claim, the test is right-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 2.9212.

P-Value

c.

The p-value corresponding to the z-score of 2.9212 is given to be equal to 0.0017.

Null hypothesis and its conclusion

d.

The null hypothesis for this test is as follows:

Null hypothesis: The proportion of adults who would feel comfortable in a self-driving vehicle is equal to 25%.

Symbolically, $H_0:p=0.25$where

p is the proportion of adults who would feel comfortable in a self-driving vehicle.

Here, the p-value equal to 0.0017 is less than the significance level of 0.05. Thus, the null hypothesis is rejected.

Conclusion of the test

e.

There is enough evidence to conclude that the proportion of adults who would feel comfortable in a self-driving vehicle is more than 25%.