Last year, a soft drink manufacturer had 21 of the market. In ...

[lb_gilbert]

Last year, a soft drink manufacturer had 21 of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 21 of the population will like the new soft drink.
 a. Set up the null and the alternative hypotheses.
  b. Determine the test statistic.
  c. Determine the p-value.
  d. At 95 confidence, test to determine if more than 21 of the population will like the new soft drink.

Question 2

Last year, 50 of MNM, Inc employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 400 employees, 180 were female.
 a. Give the null and the alternative hypotheses.
  b. At 95 confidence using the critical value approach, determine if there has been a significant reduction in the proportion of females.
  c. Show that the p-value approach results in the same conclusion as that of Part b.

[zhanghao]

Answer to Question 1

a. H0: p <= 0.21
Ha: p > 0.21
b. Test statistic Z = 1.96
c. p-value = 0.025
d. p-value = 0.025 < .05; therefore, reject Ho; more than 21 like the new drink.

Answer to Question 2

a. Ho: p  0.5
Ha: p < 0.5
b. Test statistic Z = -2.0 < -1.645; reject Ho; the proportion of female employees is significantly less than 50.
c. p-value = 0.0228 < 0.05; reject Ho.

[lb_gilbert]

Thank you

[zhanghao]

No problemo