The sequence below is a record of the replies received when college students at

Question

The sequence below is a record of the replies received when college students at ABC Universtiy were asked if they would prefer to start the fail semester early so they could have a full week fall break in October. Conduct a run test for randomness to determine if the responses are random. Complete parts (a) through (c) below. YYNNYYYNNNNMNNNYYYY (a) Identify the values of x, n_1, n_2, and r. The number of observations is x = The number of observations of the fist (Y) type is n_1 = The number of observations of the second type (N) is n_2 = The number of runs is r = (b) Determine the critical values at the alpha = 0.05 level of significance. The lower critical value is The upper critical value is (c) Conduct a hypothesis test on the randomness of the data State the appropriate conclusion. Choose the correct answer below. There is enough evidence to conclude that the sequence e not random. There is not enough evidence to conclude that the sequence is not random.

Explanation / Answer

(a) The number of observations is x = 19

The number of observations of the first (Y) type is n1 = 9

The number of observations of the second (N) type is n2 = 10

The number of runs is r = 5

(b) Since n1<20, use the run table.

The lower critical value = 5

The upper critical value = 16

(c) Since r=5 is equal to lower critical value, we reject null hypothesis that runs are random. Therefore, correct option is:

There is enough evidence to conclude that the sequence is not random.

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