A legendary story on college campuses concerns two students who miss a chemistry

Question

A legendary story on college campuses concerns two students who miss a chemistry midterm because of excessive partying but blame their absence on a flat tire. The professor allows them to take a make-up test and sends them to separate rooms to take it. The first question, worth 5 points, is quite easy. The second question, worth 95 points, asks: Which tire was it? Do students pick which tire went flat with equal proportion, or are they more likely to pick the “right front” tire than would be expected by random chance?

Describe the parameter of interest in words. Use the symbol to represent the parameter.

Write the null and alternative hypothesis for the research question in proper notation. (2 pts)

H0:

HA:

When the question was posed to a previous Stat 216 class, the following results were obtained. Calculate the observed statistic and write it using proper notation.

Left Front -6 Left Rear -4 Right Front- 14 Right Rear- 4

Calculate the standard deviation of the sample proportions under the null hypothesis.

If the standard deviation in part (e) was found to be 0.11 (that is not the correct answer), which of the following is the best interpretation of that number?

Each proportion of 28 students picking the right front tire by random chance is within 0.11 of 0.25, on average.

Each proportion of 28 students picking the right front tire by random chance is within 0.11 of 0.50, on average.

The chance a student picked the right-front tire is within 0.11 of 0.25.

The chance a student picked the right-front tire is within 0.11 of 0.50. Calculate the standardized statistic.

Use the Theory-based or One-proportion applet to obtain your p-value using the Normal distribution. Provide a screen-shot to show your work. Is the theory-based approach valid for these data? Explain.

Is the theory-based approach valid for these data? Explain.

Explanation / Answer

Null Hypotheis : H0 : = 0.25

ALternative Hypothesis : Ha : > 0.25

Here parameter of interest is the proportion of students who pick " Right Front" Tyre as the tyre busted.

HEre p^ = 14/ 28 = 0.5

standard deviation of the sample proportions under the null hypothesis

se0 = sqrt [ p(1-p)/ N] = sqrt [ 0.25 * 0.75/ 28] = 0.0818

But as per part (e), if that std. dev. is found that it is 0.11 that means that Each proportion of 28 students picking the right front tire by random chance is within 0.11 of 0.25, on average. Option a is correct.

Q. Calculate the standardized statistic.

Test statistic

Z = (p^ - 0.25)/ se0 = (0.50 - 0.25)/ 0.0818 = 3.056

p - value = Pr ( Z > 3.056) = 0.0011 (from Z - table)

As the sample size is pretty small and less than 30. The theory based work may nnot work.

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