Question

"Trydint" bubble-gum company claims that 8 out of 10 people prefer their gum to "Eklypse". Test their claim at the 90-confidence level.

The null and alternative hypothesis in symbols would be:

1. H0:p≥0.8 H1:p<0.8
2. H0:p=0.8 H1:p≠0.8
3. H0:μ=0.8 H1:μ≠0.8
4. H0:μ≤0.8 H1:μ>0.8
5. H0:μ≥0.8 H1:μ<0.8
6. H0:p≤0.8 H1:p>0.8

The null hypothesis in words would be:

1. The proportion of all people that prefer Trydint gum is 0.8
2. The average of people that prefer Trydint gum is 0.8.
3. The proportion of people in a sample that prefer Trydint gum is not 0.8
4. The proportion of all people that prefer Trydint gum is greater than 0.8.
5. The average of people that prefer Trydint gum is not 0.8.
6. The proportion of all people that prefer Trydint gum is less than 0.8.
7. The proportion of people in a sample that prefers Trydint gum is 0.8.

Based on a sample of 210 people, 166 said they prefer "Trydint" gum to "Eklypse".
The point estimate is: _____ (to 3 decimals)
The 90 % confidence interval is: ____ (to 3 decimals)

Based on this we:

1. Fail to reject the null hypothesis
2. Reject the null hypothesis

Answer 1

Here claim is that 8 out of 10 people prefer their gum to "Eklypse".

So hypothesis is

1. H0:p=0.8 H1:p≠0.8

Hence null hypothesis means that The proportion of all people that prefer Trydint gum is 0.8

Here n=210 and x=166

So

Now for 90% CI z value is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of Error is

Hence CI is

As p=0.80 is in the range we fail to reject the null hypothesis

Hence answer is

1. Fail to reject the null hypothesis