3 A company says that its premium mixture of nuts contains10

3. A company says that its premium mixture of nuts contains10% Brazil nuts, 20% cashews, 20% almonds, 10% hazelnuts and 40% peanuts. You buy a large can and separate the various kinds of nuts. The results are shown in the table below.

Type of Nut

Observed

Brazil nuts

30

Cashews

92

Almonds

16

Hazelnuts

37

Peanuts

275

TOTAL

450 nuts

Construct a relative frequency bar chart of the nut mixture (use may use excel)

State the null and alternate hypothesis for the inference test that you will be performing with this data.

Complete the table below

Type of Nut

Observed

Expected

(Observed-Expected)²/Expected

Brazil nuts

30

Cashews

92

Almonds

16

Hazelnuts

37

Peanuts

275

State all conditions that must be met to conduct this inference test.

Compute the test statistic and use the degrees of freedom to calculate the p-value.

Make your decision to either reject or fail to reject the null hypothesis using the p-value and explain why you made this decision.

State your decision in the context of the question.

Solution

H0: its premium mixture of nuts contains10% Brazil nuts, 20% cashews, 20% almonds, 10% hazelnuts and 40% peanuts

Ha: The proportion is not as above.

Two tailed chi square test.

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The table is filled up and shown below:

Chi square = 117.45

df = (r-1)(c-1) = (4-1)(2-1) =3

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p value = 0.00 <0.01

Hence at 1% significant level, we reject the nullhypothesis.

i.e. The premium mixture is not as per proportion stated and the difference is statistically significant.