1 Using the pvalue approach can the null hypothesis be rejec

1)

Using the p-value approach, can the null hypothesis be rejected for the following hypothesis test?

Test the following hypothesis for a multinomial probability distribution by using the Chi-Square goodness of fit test.

H0: Pa= 0.3, Pb = 0.5, Pc= 0.4

Ha: The probabilities are not Pa= 0.3, Pb = 0.5, Pc= 0.4

A sample of size 250 yeilded 120 in category A, 90 in category B, and 40 in category C. Use an alpha level of 0.05 and test to see whether the probabilities are as stated in H0.

Show the work please.

2)

Using the critical value approach, can the null hypothesis be rejected for the following hypothesis test?

Test the following hypothesis for a multinomial probability distribution by using the Chi-Square goodness of fit test.

H0: Pa= 0.3, Pb = 0.5, Pc= 0.4

Ha: The probabilities are not Pa= 0.3, Pb = 0.5, Pc= 0.4

A sample of size 250 yeilded 120 in category A, 90 in category B, and 40 in category C. Use an alpha level of 0.05 and test to see whether the probabilities are as stated in H0.

Show the work please.

3)

What is the difference between a Chi-Square test for the independence of two categorical variables and for the equity of population proportions?

Show the work please.

4)

What test statistic would you use for the following hypothesis test (z statistic or t statistic)? Why?

Sample 10 scoops of ice cream to see if they lead you to believe the population of scoops weigh the required 6oz.

Show the work please.

5)

What test statistic would you use for the following hypothesis test (z statistic or t statistic)? Why?

Sample 20 customers to see if they lead you to believe that average age of your customer is at 25 years of age.

Show the work please.

6)

What test statistic would you use for the following hypothesis test (z statistic or t statistic)? Why?

Sample 20 of your customers to see if they lead you to believe that less than 30% of your customers have an income of less than $25,000 a year.

Show the work please.

Thank you!

Solution

1. and 2. are not correct. It is not multinomial probability distribution. Sum of probabilites not equal to 1.

3. In chi-sqaure test of independence , chi-square test will be used while in the test for the equity of population proportions, z-statistics should be used.

4. Here sample size is too small (less than 30) so t-test statitics should be used.