In order to investigate whether cell phones are more distracting than car radios

Question

In order to investigate whether cell phones are more distracting than car radios while driving, 64 student volunteers (from a single college class) were randomly split into to a cell phone group or a control group. Each student “drove” a machine that simulated driving situations. While “driving” the simulator, a target would flash red or green at irregular intervals. Participants were instructed to press the “brake” button as soon as possible when they detected a red light. Participant response times were measured as the time between the red light appearing and pushing the brake button. While driving, the control group listened to a radio broadcast or books on tape and the cell phone group carried on a conversation about a political issue on the cell phone with someone in the next room. ?The cell phone group had an average response time of 585.2 milliseconds with a standard deviation of 89.6 milliseconds, whereas the control group had an average response time of 533.7 milliseconds and a standard deviation of 65.3 milliseconds.

(a) The output below shows the null hypothesis in symbols. Translate this statement into English for the context of this study.

(b)Assuming the t procedure is valid, a student attempts to use the “theory-based inference applet” to approximate the p-value. Explain two errors the student has made in setting up the inputs to this applet.

Error #1:

Error #2:

(c) When the correct information is entered into the applet, the theory-based test yields a p-value of 0.0055. Write a sentence interpreting this p-value – what probability does it represent??

(d) When the correct information is entered into the applet, the 95% confidence interval is found to be (12.2482, 90.7518). Write a sentence interpreting this confidence interval.

(e) Explain what is meant in the previous question by the term “95% confidence.” You should interpret “95% confidence” without using words synonymous with “confidence,” “sure,” or “probability.” Your interpretation should be in the context of this study.

(f) For each of the situations below, choose whether the p-value would become larger, smaller, or stay the same if (no explanations required and you should not perform any calculations):

* • The sample standard deviations were half as large SMALLER LARGER NO CHANGE

or

* • The cell phone group average was 5 ms longer SMALLER LARGER NO CHANGE

or

* • The sample sizes were doubled SMALLER LARGER NO CHANGE

(g) The above output displays a test statistic of t = 3.72. Write a sentence interpreting this test statistic in context – what does it measure?

Explanation / Answer

Solution

Let X = response time of control group and Y = response time of cell phone group.

Then, X ~ N(µ1, ?12) and Y ~ N(µ2, ?22), where ?12 = ?22 = ?2, say and ?2 is unknown.

Part (a)

Hypotheses: in words

Null: on an average, response time of both groups is the same vs

Alternative: Mean response time of cell phone group is greater than that of the control group. ANSWER

Part (b)

A p-value of 0.0055, is very low as compared to the general levels of significance of 5% and 1%. This implies that the chances of the two means being equal is remote, which testing parlance means that the null hypothesis is rejected. ANSWER

Part (c)

The 95% confidence interval of (12.2482, 90.7518) means that there is only 5 in a 100 chance that the mean response time of cell phone group will be more than that of the control group by less than 12,24 or more than 90.75.

Also, since this CI does not include 0, it also reconfirms that the null hypothesis is rejected

ANSWER

Part (d)

Effect on p-value

The sample standard deviations were half as large, p-value would be SMALLER

The cell phone group average was 5 ms longer p-value would be SMALLER

The sample sizes were doubled p-value would be SMALLER ANSWER

DONE

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