Question

The null hypothesis is H?: p = 0.65 The alternative Hypothesis is H? < 0.65 (or could be stated as H?<0.65 or H???<0.65). Suppose we have collected a random sample with n=680 people and that 408 have the characteristic we are interested in. Question 6: a. Calculate the value of z-statistic Z= (p?-p?)/?((p?(1-p?))/n) b. Using an ?=0.05 level of significance, look in the t-table (inf row) and find the critical value for the test of hypothesis and put a negative sign in front. (i.e. find -z?.??). Note: we use the 0.05 column as we have a one-sided test and all of the significance would be in the left tail. c. Is the test statistic value from part a less than the critical value in part b? If yes, then you will reject the null hypothesis. If no, you will fail to reject the null hypothesis. State your conclusion for the hypothesis test (This is the "classical" approach). d. In the z-table, Find the z-score that matches the z-statistic and determine the probability associated with seeing a z-score less than the z-statistic (i.e. read the value off the table). This will be the p-value. A p-value less than ?=0.05, you will reject the null hypothesis. If it is above ?=0.05, you will fail to reject the null hypothesis. State your conclusion (It should be the same conclusion as part c). This is the p-value approach.

          The null hypothesis is H?: p = 0.65

The alternative Hypothesis is H? < 0.65 (or could be stated as H?<0.65 or H???<0.65).

Suppose we have collected a random sample with n=680 people and that 408 have the characteristic we are interested in.

Question 6:

a. Calculate the value of z-statistic Z= (p?-p?)/?((p?(1-p?))/n)

b. Using an ?=0.05 level of significance, look in the t-table (inf row) and find the critical value for the test of hypothesis and put a negative sign in front. (i.e. find -z?.??). Note: we use the 0.05 column as we have a one-sided test and all of the significance would be in the left tail.

c. Is the test statistic value from part a less than the critical value in part b? If yes, then you will reject the null hypothesis. If no, you will fail to reject the null hypothesis. State your conclusion for the hypothesis test (This is the "classical" approach).

d. In the z-table, Find the z-score that matches the z-statistic and determine the probability associated with seeing a z-score less than the z-statistic (i.e. read the value off the table). This will be the p-value. A p-value less than ?=0.05, you will reject the null hypothesis. If it is above ?=0.05, you will fail to reject the null hypothesis. State your conclusion (It should be the same conclusion as part c). This is the p-value approach.

The null hypothesis is H?: p = 0.65

The alternative Hypothesis is H? < 0.65 (or could be stated as H?<0.65 or H???<0.65).

Suppose we have collected a random sample with n=680 people and that 408 have the characteristic we are interested in.

Question 6:

a. Calculate the value of z-statistic Z= (p?-p?)/?((p?(1-p?))/n)

b. Using an ?=0.05 level of significance, look in the t-table (inf row) and find the critical value for the test of hypothesis and put a negative sign in front. (i.e. find -z?.??). Note: we use the 0.05 column as we have a one-sided test and all of the significance would be in the left tail.

c. Is the test statistic value from part a less than the critical value in part b? If yes, then you will reject the null hypothesis. If no, you will fail to reject the null hypothesis. State your conclusion for the hypothesis test (This is the "classical" approach).

d. In the z-table, Find the z-score that matches the z-statistic and determine the probability associated with seeing a z-score less than the z-statistic (i.e. read the value off the table). This will be the p-value. A p-value less than ?=0.05, you will reject the null hypothesis. If it is above ?=0.05, you will fail to reject the null hypothesis. State your conclusion (It should be the same conclusion as part c). This is the p-value approach.

Added by Carmen S.

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