Supposed we are interested in understanding the mean number of M&Ms in a small bag of...

Supposed we are interested in understanding the mean number of M&Ms in a small bag of M&M. (Assume the number of M&Ms in a bag follows a normal distribution with unknown mean). You collected a sample of 16 small bags of M&M and obtain the number of counts for each package. We obtained the following sample statistics, mean number of M&M per bag is 25, and standard variation is 4. a) Construct a 90% confidence interval for the true mean number of M&M in a bag. (10pts) b) Conclude your confidence interval. (5 pts)

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 25

Population standard deviation = 2 = 4

= $\sqrt$ 4 = 2

Sample size = n = 16

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 1.645 * ( 2 / $\sqrt$ 16 )

= 0.8225

At 90% confidence interval estimate of the population mean is,

- E < < + E

25 - 0.8225 < < 25 + 0.8225

24.1775 < < 25.8225

( 24.1775 , 25.8225 )

At 90% confidence interval estimate of the population mean is : - ( 24.1775 , 25.8225 )

orchestra answered 1 year ago

Next > < Previous

Related Solutions

According to the manufacturer of M&Ms, 13% of the plain M&Ms in a bag should be...

According to the manufacturer of M&Ms, 13% of the plain M&Ms in a bag should be brown, 14% should be yellow, 13% should be red, 24% should be blue, 20% should be orange, and 16% should be green. A student randomly selected a bag of plain M&Ms. he counted the number of M&Ms that were each color and obtained the results shown in the table. Test whether plain M&Ms follow the distribution stated by M&M at the level of significance=0.05....

Question 3 In a bag of M & M’s there are 80 M & Ms, with...

Question 3 In a bag of M & M’s there are 80 M & Ms, with 11 red ones, 12 orange ones, 20 blue ones, 11 green ones, 18 yellow ones, and 8 brown ones. They are mixed up so that each candy piece is equally likely to be selected if we pick one. a) If we select one at random, what is the probability that it is red? b) If we select one at random, what is the probability...

Suppose you have a bag of M&Ms with 19 M&Ms. Suppose 4 of them are red,...

Suppose you have a bag of M&Ms with 19 M&Ms. Suppose 4 of them are red, 3 are green, and 12 are yellow. (a) If one M&M is chosen at random from the bag, find the probability that it is yellow. (b) If one M&M is chosen at random from the bag, and eaten, and then a second M&M is chosen at random from the bag, find the probability that they are both red.

According to Mars, Inc., 20% of all M&Ms produced are blue. One bag of 50 M&Ms...

According to Mars, Inc., 20% of all M&Ms produced are blue. One bag of 50 M&Ms represents the sample for this problem. The sample data can be used to perform a two-sided hypothesis test to test whether 20% of all M&Ms are blue. In one bag of 50 M&Ms, there are 14 blue M&Ms. Use this data to test whether 20% of all M&Ms are blue.

According to M&Ms are randomly mixed to have 24% blue M&MS. Suppose your bag has a...

According to M&Ms are randomly mixed to have 24% blue M&MS. Suppose your bag has a total of 57 M&Ms and 11 are blue. Assuming the distribution of total m&m is normally distribution, what is the mean and standard deviation of the sample distribution? Whats the standard score? Whats the null hypothesis and alternate hypothesis? ONE sided or two sided? What is the p-value At the 5% significance level, what would our conclusions be?

Suppose that M&M claims that each bag of Peanut M&Ms should be 18 grams and Plain...

Suppose that M&M claims that each bag of Peanut M&Ms should be 18 grams and Plain M&Ms should be 13.5 grams. a. Test the claim that M&M is shorting its customers in bags of Plain M&Ms. b. Test the claim that M&M is overfilling Peanut bag bags of M&Ms. c. Discuss your choice of ?. i. Why did you choose the ? you did? ii. If you had chosen a different ?, would it have affected your conclusion? Total Plain...

1. Let M denote set of m&ms in a bag. This consist of red, yellow, green,...

1. Let M denote set of m&ms in a bag. This consist of red, yellow, green, blue and brown candies. a. Device on equivalence relation on M. b. Define relation R on M by: aRb if and only if either: a is green or b is blue, or, a is yellow abd b is not yellow. Is R symmetric, reflexive, transitive or anti-symmetric? Explain. 2. On set Zx(Z not including {0}) define relation R (a,b) a,b e Z, b#0 as...

The company that makes M&Ms claims that the 6 colors are evenly distributed in each bag....

The company that makes M&Ms claims that the 6 colors are evenly distributed in each bag. Conduct a goodness of fit test to determine whether this claim is true or not. Choose two alpha values (level of significance.) Colors of M&Ms: Blue, Green, Yellow, Brown, Red, Orange . Total=6 Observed Frequency: Blue=7, Green=7, Yellow=3, Brown=2, Red=4, Orange=2 Total=25 A) State the null hypothesis B) what is expected frequency what is (O-E)^2/E C)Using the x^2 distribution table, find the critical value...

The company that makes M&Ms claims that the 6 colors are evenly distributed in each bag....

We are interested in understanding if there is a difference between the consumption of personal training...

We are interested in understanding if there is a difference between the consumption of personal training between two of our tapestry segments. Segment 1 uses personal training 6.3 times on average per year (n=1000). Segment 2 uses personal training 5.8 times on average per year (n=850). The standard deviation for segment 1 is 2.3 and for segment 2 is 3.2. Is this a significant difference? Why or why not? Assume we are looking for 99% significance.

Subjects