A researcher conducts a small lab study including two variables, the amount of a

Question

A researcher conducts a small lab study including two variables, the amount of alcohol consumption and the number of errors automobile drivers make. Before the driving test, subjects drink a glass of orange juice with a controlled amount of vodka—an alcoholic liquor. The drivers’ performance is measured by the number of errors on a driving simulator; five subjects receive different amounts of vodka—from 0 to 4 ounces. The following results were obtained.

The researcher wants to test if there is a relationship between the amount of alcohol consumption and the number of errors automobile drivers make. Perform the hypothesis testing to see if the relationship is significant. Show all your work.

Analyze the data using SPSS. Copy and paste the SPSS table. Using the p-value, make a conclusion.

Please show all the necessary steps. If the necessary steps are missing, you will not get full credits even if your final answer is correct. On the other hand, even if your final answer is wrong, you may still get partial credit for the proper steps.

Subject ID Alcolhol # of Errors 1 0 1 2 1 2 3 2 3 4 3 5 5 4 4

Explanation / Answer

Solution:

Here, we have to use t test for checking whether there is a relationship between the amount of alcohol consumption and the number of errors automobile drivers make.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is no any statistically significant relationship exists between the amount of alcohol consumption and the number of errors automobile drivers make.

Alternative hypothesis: Ha: There is a statistically significant relationship exists between the amount of alcohol consumption and the number of errors automobile drivers make.

H0: = 0 versus Ha: 0

This is a two tailed test.

The test statistic formula is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

We have following data with correlation coefficient and sample size given as below:

Alcohol

Number of errors

0

1

1

2

2

3

3

5

4

4

Correlation coefficient = r = 0.90

Sample size = n = 5

df = n – 2 = 5 – 2 = 3

t = 0.90*sqrt(5 - 2)/sqrt(1 - 0.90^2)

t = 3.576237

P-value = 0.037386

We assume = 0.05

P-value < = 0.05

So, we reject the null hypothesis H0 at 5% level of significance.

We reject the null hypothesis that there is no any statistically significant relationship exists between the amount of alcohol consumption and the number of errors automobile drivers make.

There is sufficient evidence to conclude that there is a statistically significant relationship exists between the amount of alcohol consumption and the number of errors automobile drivers make.

SPSS table is given as below:

Correlations

Alcohol

Number of errors

Alcohol

Pearson Correlation

1

.900*

Sig. (2-tailed)

.037

N

5

5

Number of errors

Pearson Correlation

.900*

1

Sig. (2-tailed)

.037

N

5

5

*. Correlation is significant at the 0.05 level (2-tailed).

We assume = 0.05

P-value < = 0.05

There is sufficient evidence to conclude that there is a statistically significant relationship exists between the amount of alcohol consumption and the number of errors automobile drivers make.

Alcohol

Number of errors

0

1

1

2

2

3

3

5

4

4

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