MOST OF THE QUESTIONS ARE ALREADY ANSWERED PLEASE ANSWER THE OTHERS :)

M&M Color	Frequency	Proportion (decimal to 4 places)
Red	38	0.1413
Orange	72	0.2677
Yellow	28	0.1041
Green	38	0.1413
Blue	63	0.2342
Brown	30	0.1115
Total	269	1

1. Assuming the true proportion of blue M&Ms is 10%, verify the conditions for claiming the sampling distribution of sample proportions for the proportion of blue M&Ms is normal with n equal to the class's sample size.

1. What is the mean of the sampling distribution?

1. What is the standard deviation of the sampling distribution? Show your calculations and round to two decimal places.

1. On the first page of blank normal distributions, complete distribution 1 by labeling the mean and each standard deviation from the mean with the correct values (these values represent the proportion of blue M&Ms in a bag).
2. Using the Empirical rule, what proportions of blue M&Ms mark the middle 95% of bags?

1. Using StatCrunch, find each of the following:
   1. There is a 5% chance of getting a bag with more thanthis proportion of blue M&Ms.

1. There is a 5% chance of getting a bag with less thanthis proportion of blue M&Ms.

1. There is a 5% chance of getting a bag with more or less thanthese proportion of blue M&Ms.

1. Add the results of 16 to the normal curve 1. Use the following colors to label and shade the graph accordingly:
   1. Blue
   2. Black
   3. Red
2. On the first page of blank normal distributions, complete distribution 2 by labeling the mean and each standard deviation from the mean with the correct values (these values represent the proportion of blue M&Ms in a bag).
3. Using StatCrunch, compute a 90% confidence interval about the mean. What are the lower limit, upper limit, and margin of error?

Lower Limit =

Upper Limit =

Margin of Error =

1. InBlue, Add the 90% confidence interval to normal curve 2. Clearly label the lower limit, upper limit, and margin of error.
2. Compare the two normal distributions you made. How does the 90% confidence interval compare to your results from question 16? Why do you think this is?

1. Using StatCrunch, find a 95% confidence interval about the mean. What are the lower limit, upper limit, and margin of error?

Lower Limit =

Upper Limit =

Margin of Error =

1. InRed, add the 95% confidence interval to the normal 2.
2. How does the 95% confidence interval compare to your results from question 16? Why do you think this is?

1. Based on the class's sample proportion of blue M&Ms, from number 14, and the values found in questions 18 - 23, do you think we should reject that the true proportion of blue M&Ms is 10%? Why or why not?

Part 3

Resources needed

• Second page of the blank normal curves (last pages of this document - print before beginning part 2)
• StatCrunch

1. On the second page of normal distributions, complete distribution 3 and 4 by labeling the mean and each standard deviation from the mean with the same values as the first two distributions. Below the mean and standard deviation, write the associated values for thestandardnormal distribution.
2. According to theSAS Software company, the proportion of each color has shifted throughout the years. What was the color distribution in the late 1990's? 2008? 2017? Use thisSummary Article to complete the table below.

M&M Color	Proportion (1990's)	Proportion (2008)	Proportion (2017) average the two factory's results
Red
Orange
Yellow
Green
Blue
Brown

1. In the 1990's, the SAS software company claimed that only 10% of M&M's were blue. A Davidson-Davie class of MAT 152 students collected some data and found there were blue M&Ms out of total M&Ms. Is there sufficient evidence to conclude at the = 0.10 level of significance that the proportion of blue M&Ms has changed since the 1990's. The following steps walk you through the classical approach for hypothesis testing.
   1. State the null and alternative hypotheses.

1. State the level of significance.

1. Find the critical value(s) for this level of significance. Add the critical value(s) and shade the critical region(s) on distribution 3.
2. Find the test statistic and add it to distribution 3. You will need to extend the graph to label this point. Compare the test statistic with the critical value(s).

1. Decision:
2. Conclusion in context:

1. In the 1990's, the SAS software company claimed that only 10% of M&M's were blue. A Davidson-Davie class of MAT 152 students collected some data and found there were blue M&Ms out of total M&Ms. Is there sufficient evidence to conclude at the = 0.10 level of significance that the proportion of blue M&Ms has changed since the 1990's. The following steps walk you through the p-value approach for hypothesis testing.
   1. State the null and alternative hypotheses.

1. State the level of significance.

1. Locate the critical region on distribution 3. This shaded area is equal to the level of significance. Label this region as alpha.
2. Calculate the p-value. Shade and label the p-value on distribution 3. Remember, p-value is the probability of observing a sample statistic as extreme or more extreme than the sample statistics we observed under the assumption the null hypothesis is true.
3. Compare the p-value and level of significance.

1. Decision:
2. Conclusion in context:
3. In the 1990's, the SAS software company claimed that only 10% of M&M's were blue. A Davidson-Davie class of MAT 152 students collected some data and found there were blue M&Ms out of total M&Ms. Is there sufficient evidence to conclude at the = 0.05 level of significance that the proportion of blue M&Ms hasincreased since the 1990's. The following steps walk you through the p-value approach for hypothesis testing.
   1. State the null and alternative hypotheses.

1. State the level of significance.

1. Find the critical value for this level of significance. Add the critical value and shade away from the mean on distribution 4. You will need to extend the graph. The shaded area is equal to the level of significance. Label this region as alpha.
2. Calculate the p-value. Shade and label the p-value on distribution 4. Remember, p-value is the probability of observing a sample statistic as extreme or more extreme than the sample statistics we observed under the assumption the null hypothesis is true.
3. Compare the p-value and level of significance.

1. Decision:
2. Conclusion in context:
3. Compare all 4 distributions you made. What's the same? What's different? What can you conclude about how each of the following relate to each other?

• Sampling distributions of sample proportions
• Confidence intervals
• Hypothesis testing

Specifically, address

• Critical values
• Lower limits and upper limits of confidence intervals
• Test statistics
• Sample proportion
• P-values
• Confidence levels