Question

A candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 200 jelly beans. If you receive a bag with 40 blue jelly beans, would you be doubtful of the company's claim? Answer by calculating the appropriate z-score. Round to the nearest hundredth when necessary.

Answer 1

Doubtful.

Explanation:

Our values are,

`P=0.15 \rightarrow 15\%`Jelly Bean Mix.

The sample for us is n=200

And our proportion (x) is 40 .

We can calculate with this dates the sample proportion and make he test statistic.

`p=(x)/(n) = (40)/(200) = 0.20`

`H_0:P=0.15`

`H_1:P \\eq 0.15`

We use the formula for Test statistic, that is given by,

`z= \frac{p-P}{\sqrt{(P-(1-P))/(n)}}`

`z= \frac{0.20-0.15}{\sqrt{(0.15(1-0.15))/(200)}}`

`z= 1.98`

We see that our P-value: 0.048 (From the Table)

We note that p-value is less than 0.05, so we should to rejecyt the null hypothesis and conclude that the calim is doubtful