Different Proportion of M&M Candies in Each Colour between Two Sample Proportions - Research Paper Example

There were 1535 blue candies in the bag out of 7356 candies and the proportion of blue candies is 0.2087. The 95% Confidence Interval is (0.1994, 0.218). There were 1587 orange candies in the bag out of 7356 candies and the proportion of orange candies is 0.2157. The 95% Confidence Interval is (0.2063,0.2251). There were 1320 green candies in the bag out of 7356 candies and the proportion of green candies is 0.1794. The 95% Confidence Interval is (0.1707, 0.1882). There were 925 yellow candies in the bag out of 7356 candies and the proportion of yellow candies is 0.1257. The 95% Confidence Interval is (0.1182, 0.1333).

There were 990 red candies in the bag out of 7356 candies and the proportion of red candies is 0.1346. The 95% Confidence Interval is (0.1268, 0.1424). There were 999 brown candies in the bag out of 7356 candies and the proportion of brown candies is 0.1358. The 95% Confidence Interval is (0.128, 0.1436). The sample size in estimating the proportion is 438. In testing whether the given sample proportion of blue candies (0.2087) matches with the population proportion 0.24 of blue candies. The hypothesis is rejected (Z=-6.291) since the observed value is less than the expected value -1.96. Hence there is a significant difference between the sample proportion and population proportion.

In testing whether the given sample proportion of orange candies (0.2157) matches with the population proportion 0.2 of orange candies, the hypothesis is rejected (Z=3.3754) since an observed value is greater than the expected value 1.96. Hence there is a significant difference between the sample proportion of orange candies and population proportion of orange candies. In testing whether the given sample proportion of green candies (0.1794) matches with the population proportion 0.16 of green candies, the hypothesis is rejected (Z=4.5492) since the observed value is greater than the expected value 1.96.