Question

Asked Dec 2, 2019

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"Trydint" bubble-gum company claims that 5 out of 10 people prefer their gum to "Eklypse". Test their claim at the 99 confidence level.

The null and alternative hypothesis in symbols would be:

H

0

:

μ

≥

0.5

H0:μ≥0.5

H

1

:

μ

<

0.5

H1:μ<0.5

H

0

:

p

≥

0.5

H0:p≥0.5

H

1

:

p

<

0.5

H1:p<0.5

H

0

:

μ

≤

0.5

H0:μ≤0.5

H

1

:

μ

>

0.5

H1:μ>0.5

H

0

:

p

=

0.5

H0:p=0.5

H

1

:

p

≠

0.5

H1:p≠0.5

H

0

:

p

≤

0.5

H0:p≤0.5

H

1

:

p

>

0.5

H1:p>0.5

H

0

:

μ

=

0.5

H0:μ=0.5

H

1

:

μ

≠

0.5

H1:μ≠0.5

The null hypothesis in words would be:

The proportion of all people that prefer Trydint gum is 0.5

The proportion of all people that prefer Trydint gum is greater than 0.5.

The proportion of all people that prefer Trydint gum is less than 0.5.

The proportion of people in a sample that prefer Trydint gum is not 0.5

The average of people that prefer Trydint gum is 0.5.

The average of people that prefer Trydint gum is not 0.5.

The proportion of people in a sample that prefers Trydint gum is 0.5.

Based on a sample of 290 people, 121 said they prefer "Trydint" gum to "Eklypse".

The point estimate is: (to 3 decimals)

The 99 % confidence interval is: to (to 3 decimals)

Based on this we:

Fail to reject the null hypothesis

Reject the null hypothesis

Step 1

**Stating the appropriate null and alternative hypotheses:**

It was found that 5 out of 10 people prefer gum to Eklypse.

The hypotheses are given below:

*Null hypothesis:*

*H*_{0}** : p = 0.50.**

**That is, the proportion of all people who prefer Trydint gum to Eklypse is equal to 0.50.**

*Alternative hypothesis:*

*H*_{a}** : p ≠0.50.**

That is, the proportion of people who prefer gum to Eklypse is not equal to 0.50.

Step 2

**Finding the point estimate:**

Let *p* be the sample proportion.

It was found that, 121 people prefer Trydint gum to Eklypse out of a sample of 290 people.

The sample proportion(point estimate), *p* is calculated below.

Step 3

The sample proportion is 0.417.

The sample size is 290.

Since the required confidence interval is 99%, the two-tailed *z* value at 0.01 lev...

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