Question

"Trydint" bubble-gum company claims that 6 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:μ=0.6 H1:μ≠0.6
2. H0:p≥0.6 H1:p<0.6
3. H0:μ≤0.6 H1:μ>0.6
4. H0:μ≥0.6 H1:μ<0.6
5. H0:p=0.6 H1:p≠0.6
6. H0:p≤0.6 H1:p>0.6

The null hypothesis in words would be:

1. The proportion of all people that prefer Trydint gum is 0.6
2. The proportion of all people that prefer Trydint gum is less than 0.6.
3. The average of people that prefer Trydint gum is not 0.6.
4. The proportion of people in a sample that prefer Trydint gum is not 0.6
5. The average of people that prefer Trydint gum is 0.6.
6. The proportion of all people that prefer Trydint gum is greater than 0.6.
7. The proportion of people in a sample that prefers Trydint gum is 0.6.

Based on a sample of 470 people, 267 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

a) Option - e) H₀: p = 0.6

                      H₁: p 0.6

Option - a) The proportion of people that prefer Trydint gum is 0.6.

The point estimate is = 267/470 = 0.568

At 90% confidence interval the critical value is z_0.05 = 1.645

The 90% confidence interval for population proportion is

+/- z_0.05 * sqrt(p(1 - p)/n)

= 0.568 +/- 1.645 * sqrt(0.6 * (1 - 0.6)/470)

= 0.568 +/- 0.037

= 0.531, 0.605

Since the interval contains the hypothesized value 0.6, so we should not reject the null hypothesis.

Option - a) Fail to reject the null hypothesis.