Question

A fund manager wants to know if it is equally likely that the Nasdaq Average will go up each day of the week. For each day of the week, the fund manager observes the following number of days when the Nasdaq Average goes up.

Day of the Week	Observed
Monday	192
Tuesday	189
Wednesday	202
Thursday	199
Friday	218

For the goodness-of-fit test, the null and alternative hypotheses are ________.

		H0: p1 = p2 = p3 = p4 = 1/4, HA: Not all population proportions are equal to 1/4
		H0: p1 = p2 = p3 = p4 = p5 = 1/5, HA: Not all population proportions are equal to 1/5
		H0: p1 = p2 = p3 = p4 = p5 = 1/4, HA: Not all population proportions are equal to 1/4
		H0: p1 = p2 = p3 = p4 = 1/5, HA: Not all population proportions are equal to 1/5

(No excel work)

Answer 1

A fund manager wants to know if it is equally likely that the Nasdaq average will go up each day of the week.

For each day of the week, the fund manager observes the number of days, when the Nasdaq average goes up.

Now, the average is likely to go up on five of the days, namely monday, tuesday, wednesday, thursday and friday.

If they are equally likely to go up on any of the days, then the probability of going up on each of 5 days, is 1/5, because there are 5 possible days, and we are considering one single day.

If these probabilities are

Then the claim is that all of them is equal to 1/5.

The alternate hypothesis is that at least one of them is not equal to 1/5, or in other words, not all population proportions are equal to 1/5.

So, for the goodness-of-fit test, the null and alternative hypothesis are respectively

option (b)

.