A company claims they produce their mixed bag of candies so that, of the candies in the bag, 20percent are dark chocolate, 60 percent are milk chocolate, and 20 percent are white chocolate. In a random sample of candies of size 50, the counts are as follows: 6 dark, 32 milk, and 12 white. Is there convincing evidence that the distribution of candies is incorrect at the alpha = 0.1 significance level?

(a) State

Ho:The distribution of mixed candies is NOT evenly distributed.

The claimed distribution of mixed candies is correct.

The distribution of mixed candies is evenly distributed.

There is an association between percentage and candy type.

The claimed distribution of mixed candies is NOT correct.

There is NO association between percentage and candy type.

Ha:The distribution of mixed candies is NOT evenly distributed.

The claimed distribution of mixed candies is NOT correct.

There is NO association between percentage and candy type.

The distribution of mixed candies is evenly distributed.

There is an association between percentage and candy type.

The claimed distribution of mixed candies is correct.

DarkMilkWhiteExpected Counts19.2

10

30

1.2

2.4

19.2

10

30

1.2

2.4

19.2

10

30

1.2

2.4

We will conduct a2-Prop Z Test

X2 GOF - Test

T Test

1-Prop Z Test

X2 Test

2-Samp T Test

(b) Plan:

Random -All OBSERVED counts are at least 5 so this condition is met.

We assume 50 candies is less than 10% of all candies.

There are less than 500 total candies, so 50 is NOT less than 10%

Not stated in the problem.

We cannot assume 50 candies is less than 10% of all candies.

All EXPECTED counts are at least 5 so this condition is met.

Stated in the problem, "random sample of 50 candies"

All EXPECTED counts are NOT at least 5 so this condition is NOT met.

All OBSERVED counts are at NOT least 5 so this condition is NOT met.

10% -All OBSERVED counts are at least 5 so this condition is met.

We assume 50 candies is less than 10% of all candies.

There are less than 500 total candies, so 50 is NOT less than 10%

Not stated in the problem.

We cannot assume 50 candies is less than 10% of all candies.

All EXPECTED counts are at least 5 so this condition is met.

Stated in the problem, "random sample of 50 candies"

All EXPECTED counts are NOT at least 5 so this condition is NOT met.

All OBSERVED counts are at NOT least 5 so this condition is NOT met.

Large Counts -We cannot assume 50 candies is less than 10% of all candies.

All EXPECTED counts are at least 5 so this condition is met.

Stated in the problem, "random sample of 50 candies"

Not stated in the problem.

There are less than 500 total candies, so 50 is NOT less than 10%

All OBSERVED counts are at least 5 so this condition is met.

We assume 50 candies is less than 10% of all candies.

All EXPECTED counts are NOT at least 5 so this condition is NOT met.

All OBSERVED counts are at NOT least 5 so this condition is NOT met.

Since all conditionsHAVE

HAVE NOT

been met, we will conduct aX2 GOF - Test

2-Prop Z Test

T Test

1-Prop Z Test

X2 Test

2-Samp T Test

.

(c) Do:

X2 =2.1333

0.3442

2

3

0.1238

5.3684

P-Value =2.1333

0.3442

2

3

0.1238

5.3684

df =2.1333

0.3442

2

3

0.1238

5.3684

(d) Conclude:

Since our P-value isLESS THAN

GREATER THAN

our alpha value of0.1

0.05

0.01

, weREJECT

DO NOT REJECT

Ho. ThereIS

IS NOT

convincing evidence thatThe distribution of mixed candies is NOT evenly distributed.

The claimed distribution of mixed candies is correct.

The distribution of mixed candies is evenly distributed.

There is an association between percentage and candy type.

The claimed distribution of mixed candies is NOT correct.

There is NO association between percentage and candy type.

.