Part I: The scores of a sample of 5 students, selected from a large population, are given below.

Score

70

80

60

90

75

(a) Determine a point estimate for the variance of the population.

(b). Using the p-value approach, at the 10% level of significance, test to determine if the variance of the population is less than or equal to 50. (Make sure that you clearly formulate the null and alternative hypotheses)

Part II: The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party

Support

Democrats

100

Republicans

120

Independents

80

We are interested in determining whether or not the opinions of the individuals of the three groups are equally distributed. Formulate a suitable null and alternative hypothesis and test at the 5% level.