10) The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injuredautomobile drivers were intoxicated. A random sample of 50 records of automobile driver fatalities in a certain county showedthat 33 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcoholis less than 77% in Kit Carson County? Use a = 0.05.A USE SALT(a) What is the level of significance?.05State the null and alternate hypotheses.O Ho: P = 0.77; H: p> 0.77• Ho:P = 0.77; H: p< 0.77O H: p = 0.77: H,: p 0.77O H,: P< 0.77; H,: p = 0.77(b) What sampling distribution will you use?O The standard normal, since np < 5 and ng < 5.The Student's t, since np < 5 and ng < 5.O The Student's t, since np > 5 and ng > 5.O The standard normal, since np > 5 and ng > 5.What is the value of the sample test statistic? (Round your answer to two decimal places.) (b) What sampling distribution will you use?O The standard normal, since np < 5 and nq < 5.The Student's t, since np < 5 and nq < 5.O The Student's t, since np > 5 and nq > 5.O The standard normal, since np >5 and nq > 5.What is the value of the sample test statistic? (Round your answer to two decimal places.)(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)Sketch the sampling distribution and show the area corresponding to the P-value.

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Description: 10) The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injuredautomobile drivers were intoxicated. A random sample of 50 records of automobile driver fatalities in a certain county

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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10)

The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured
automobile drivers were intoxicated. A random sample of 50 records of automobile driver fatalities in a certain county showed
that 33 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol
is less than 77% in Kit Carson County? Use a = 0.05.
A USE SALT
(a) What is the level of significance?
.05
State the null and alternate hypotheses.
O Ho: P = 0.77; H: p> 0.77
• Ho:P = 0.77; H: p< 0.77
O H: p = 0.77: H,: p 0.77
O H,: P< 0.77; H,: p = 0.77
(b) What sampling distribution will you use?
O The standard normal, since np < 5 and ng < 5.
The Student's t, since np < 5 and ng < 5.
O The Student's t, since np > 5 and ng > 5.
O The standard normal, since np > 5 and ng > 5.
What is the value of the sample test statistic? (Round your answer to two decimal places.)

(b) What sampling distribution will you use?
O The standard normal, since np < 5 and nq < 5.
The Student's t, since np < 5 and nq < 5.
O The Student's t, since np > 5 and nq > 5.
O The standard normal, since np >5 and nq > 5.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.

Expert Solution

Step 1

Given Information:

Proportion $p = 0.77$

Sample size $n = 50$

Out of which $x = 33$ records involved an intoxicated driver.

Claim: Population proportion of driver fatalities related to alcohol is less than 77%.

Significance level $α = 0.05$

(b) Since, $n p > 5$ i.e., $50 (0.77) = 38.5 > 5$ and $n q > 5$ i.e., $n q = n (1 - p) = 50 (1 - 0.77) = 11.5 > 5$

We use standard normal distribution.

Sample proportion is the number of successes divided by the sample size. It is given by the formula $\hat{p} = \frac{x}{n}$

So, sample proportion is:

$\hat{p} = \frac{33}{50} = 0.66$

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