Question

"Trydint" bubble-gum company claims that 8 out of 10 people prefer their gum to "Eklypse". Test their claim at the 95 confidence level. The null and alternative hypothesis in symbols would be: H 0 : μ ≤ 0.8 H 1 : μ > 0.8 H 0 : p ≤ 0.8 H 1 : p > 0.8 H 0 : μ = 0.8 H 1 : μ ≠ 0.8 H 0 : p ≥ 0.8 H 1 : p < 0.8 H 0 : μ ≥ 0.8 H 1 : μ < 0.8 H 0 : p = 0.8 H 1 : p ≠ 0.8

The null hypothesis in words would be:

The proportion of all people that prefer Trydint gum is greater than 0.8.

The proportion of people in a sample that prefer Trydint gum is not 0.8

The average of people that prefer Trydint gum is not 0.8.

The proportion of people in a sample that prefers Trydint gum is 0.8.

The proportion of all people that prefer Trydint gum is less than 0.8.

The average of people that prefer Trydint gum is 0.8.

The proportion of all people that prefer Trydint gum is 0.8

Based on a sample of 130 people, 91 said they prefer "Trydint" gum to "Eklypse".

The point estimate is: (to 3 decimals)

The 95 % confidence interval is: to (to 3 decimals)

Based on this we:

Reject the null hypothesis

or

Fail to reject the null hypothesis

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses:

H 0 : p = 0.8 H 1 : p ≠ 0.8

Null hypothesis in words:

The proportion of all people that prefer Trydint gum is 0.8

Point estimate = 0.7

95% confidence interval: (0.621, 0.779)

Reject the null hypothesis; Since 0.8 is not the part of the interval.