Question

please type anwser if possible I have trouble reading hand written notes

Mars Inc., makers of M&M’s candies, claims that they produce plain M&M’s with the following distribution:Brown: 30%Red: 20%Yellow: 20%Orange: 10%Green:10%Blue: 10%A bag of plain M&M’s was selected randomly from the grocery store shelf, and the color counts were as follows:Brown: 16Red:11Yellow: 19Orange: 5Green:7Blue: 3(a)You want to conduct an appropriate test of the manufacturer’s claim for the proportion of yellow M&M’s. Identify the population and parameter of interest. Then state hypotheses.(3 pts).(b)Calculate the sample proportion of yellow M&M’s in the sample bag.Round to the nearestthousandth.(2 pts).

(c)Checkthe conditions for performing the significance test.(3 pts)(c) Calculate the test statistic and the P-value using your calculator.(2 pts)(d) What conclusion can you make about the true proportion of plain yellow M&M’s? Explain.(3 pts)(e)Based on this sample, construct and interpret a 90% confidence interval for the proportion of yellow M&M’s candies produced by Mars.Use your calculator to calculate the interval.(3 pts)

Answer 1

(a)You want to conduct an appropriate test of the manufacturer’s claim for the proportion of yellow M&M’s. Identify the population and parameter of interest. Then state hypotheses.(3 pts).

The population is all the M&M’s candies and the parameter of interest is yellow M&M’s.

The hypothesis being tested is:

H₀: p = 0.20

H_a: p ≠ 0.20

(b)Calculate the sample proportion of yellow M&M’s in the sample bag.Round to the nearestthousandth.(2 pts).

The sample proportion of yellow M&M’s = 19/(16 + 11 + 19 + 5 + 7 + 3) = 0.311

(c)Checkthe conditions for performing the significance test.(3 pts)

n*p = 61*0.311 = 19 10

n*(1 - p) = 61*(1 - 0.311) = 42 10

The conditions are met.

(c) Calculate the test statistic and the P-value using your calculator.(2 pts)

The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.311 - 0.20)/√0.20(1-0.20)/0.20 = 2.18

The p-value is 0.0295.

(d) What conclusion can you make about the true proportion of plain yellow M&M’s? Explain.(3 pts)

Since the p-value (0.0295) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that p ≠ 0.20.

(e)Based on this sample, construct and interpret a 90% confidence interval for the proportion of yellow M&M’s candies produced by Mars.Use your calculator to calculate the interval.(3 pts)

The 90% confidence interval will be:

= p ± z*(√p(1-p)/n)

= 0.311 ± 1.645*(√0.311(1-0.311)/61)

= (0.2139, 0.409)

Please give me a thumbs-up if this helps you out. Thank you!