Maria Huey

2021-12-16

A company that manufactures toothpaste is studying five different package designs.

Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred.

The following data were obtained. Do the data confirm the belief that one design is just as likely to be selected as another? Explain.

Andrew Reyes

Beginner2021-12-17Added 24 answers

Step 1

The probability is the number of favorable outcomes divided by the number of possible outcomes:

It does not appear that the data confirm the belief that one desing is just as likely to be selected as another, because design 4 is preferred 40 times, while design 1 is only preferred 5 times and this is a very large difference in a group of 100.

accimaroyalde

Beginner2021-12-18Added 29 answers

Step 1

The assumption made is that all the 5 different packages are equally likely, i.e. the probability of selecting a package is$\frac{1}{5}=0.20$

The probability distribution is shown below.

According to the probability distribution:

The probability of a person preferring design 1 is,

$P(X=1)=0.10$

The probability of a person preferring design 2 is,

$P(X=2)=0.05$

The probability of a person preferring design 3 is,

$P(X=3)=0.30$

The probability of a person preferring design 4 is,

$P(X=4)=0.40$

The probability of a person preferring design 1 is,

$P(X=5)=.15$

So it can be seen that the probability of preferring any of the 5 designs are not same.

Thus, the designs are not equally likely.

The correct option is "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

$$\begin{array}{|ccc|}\hline \text{Design}(X)& \text{number of times Preferred}(f(x))& P(X)\\ 1& 10& 0.10\\ 2& 5& 0.05\\ 3& 30& 0.30\\ 4& 40& 0.40\\ 5& 15& 0.15\\ Total=& 100& 1.00\\ \hline\end{array}$$

The assumption made is that all the 5 different packages are equally likely, i.e. the probability of selecting a package is

The probability distribution is shown below.

According to the probability distribution:

The probability of a person preferring design 1 is,

The probability of a person preferring design 2 is,

The probability of a person preferring design 3 is,

The probability of a person preferring design 4 is,

The probability of a person preferring design 1 is,

So it can be seen that the probability of preferring any of the 5 designs are not same.

Thus, the designs are not equally likely.

The correct option is "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

nick1337

Expert2021-12-27Added 777 answers

Step 1

Given:

Probability (one number)

Step 2

Null hypothesis :

Alternative hypothesis :

It is a two tailed test

Step 3

Apply chi square test:

Step 4

Degree of freedom

so, it rejects null hypothesis

We have insufficient evidence to conclude that one design is just as likely to be selected as another.

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