Question

A website reported that 28 % of drivers 18 and older admitted to texting while driving in 2009. In a random sample of 400 drivers 18 years and older drawn in 2010, 109 of the drivers said they texted while driving. Complete parts a through c below.

**a.** Construct a 90 % confidence interval to
estimate the actual proportion of people who texted while driving
in 2010.

A 90 % confidence interval to estimate the actual proportion has a lower limit of _ and an upper limit of _.

**b.** What is the margin of error for this
sample?

**c.** Is there any evidence that this proportion
has changed since 2009 based on this sample?

Because the confidence interval found in part a ___ the reported proportion from 2009, this sample ___ evidence that this proportion has changed since then.?

Answer #1

The statistical software output for this problem is:

**One sample proportion summary confidence
interval:**

p : Proportion of successes

Method: Standard-Wald

**90% confidence interval results:**

Proportion |
Count |
Total |
Sample Prop. |
Std. Err. |
L. Limit |
U. Limit |
---|---|---|---|---|---|---|

p | 109 | 400 | 0.2725 | 0.022262286 | 0.2358818 | 0.3091182 |

Hence,

a) 90% confidence interval:

Lower limit = 0.236

Upper limit = 0.309

b) Margin of error = (0.309 - 0.236)/2 = 0.0365

c) Contains; Do not provide

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