1.We have been told that 45% of all Reese's Pieces are orange, whereas 27.5% are brown and 27.5% are yellow. To investigate this hypothesis, some students counted the number of candies of each color in a bag of 500 Reese's Pieces. They found 198 orange candies, 155 brown candies, and 147 yellow candies. Test the hypothesis that the percentage of orange Reese's Pieces is different from 45% by stating the hypotheses, calculating the test statistic and p-value, and indicating what decision you would make and what it means using a significance level of = .01.

i.Using correct statistical notation, state the null and alternative hypotheses:

ii.Report the Test Statistic rounded to two decimals:

iii.Report the p-value (rounded to four decimals), including drawing, labeling, and shading the appropriate distribution to show the p-value and test statistic.

iv.Circle your conclusion about the Null Hypothesis:

Reject the Null HypothesisFail to Reject the Null Hypothesis

v.Do the data support the claim that 45% of Reese's Pieces are orange? Answer with complete sentences and specifically address the claim. Support your decision by explaining the statistical evidence.

2.The weights at birth of five randomly chosen baby hippopotamuses born in captivity were 75, 99, 107, 82, and 63 pounds. Assume the distribution of weights is normally distributed.

Scientists suspect that baby hippos born in captivity weigh more than those born in the wild, on average. Past sample data shows that baby hippopotamuses born in the wild have a mean weight of 76 pounds. Using the = .10 significance level, test the claim that hippos born in captivity weigh more, on average. Perform the appropriate hypothesis test by stating the hypotheses, calculating the test statistic and p-value, and indicating what decision you would make and what it means.

i.Using correct statistical notation, state the null and alternative hypotheses:

ii.Report the Test Statistic rounded to two decimals:

iii.Report the p-value (rounded to four decimals), including drawing, labeling, and shading the appropriate distribution to show the p-value and test statistic.

iv.Circle your conclusion about the Null Hypothesis:

Reject the Null HypothesisFail to Reject the Null Hypothesis

v.Do the data support the claim? Answer with complete sentences and specifically address the claim. Support your decision by explaining the statistical evidence.

3.To test the effectiveness of a new drug designed to relieve flu symptoms, 200 patients were randomly selected and divided into two equal groups. One group of 100 patients was given a pill containing the drug while the other group of 100 was given a placebo. What can we conclude about the effectiveness of the drug if 62 of those actually taking the drug felt a beneficial effect while 41 of the patients taking the placebo felt a beneficial effect? Use =

0.05 to test the drug's effectiveness.

i.Using correct statistical notation, state the null and alternative hypotheses:

ii.Report the Test Statistic rounded to two decimals:

iii.Report the p-value (rounded to four decimals), including drawing, labeling, and shading the appropriate distribution to show the p-value and test statistic.

iv.Circle your conclusion about the Null Hypothesis:

Reject the Null HypothesisFail to Reject the Null Hypothesis

v.Do the data support the claim? Answer with complete sentences and specifically address the claim. Support your decision by explaining the statistical evidence.