Question

"Trydint" bubble-gum company claims that 3 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 : p ≤ 0.3 H 1 : p > 0.3 H 0 : μ = 0.3 H 1 : μ ≠ 0.3 H 0 : μ ≥ 0.3 H 1 : μ < 0.3 H 0 : μ ≤ 0.3 H 1 : μ > 0.3 H 0 : p = 0.3 H 1 : p ≠ 0.3 H 0 : p ≥ 0.3 H 1 : p < 0.3 The null hypothesis in words would be: The average of people that prefer Trydint gum is not 0.3. The proportion of all people that prefer Trydint gum is less than 0.3. The proportion of people in a sample that prefers Trydint gum is 0.3. The proportion of people in a sample that prefer Trydint gum is not 0.3 The proportion of all people that prefer Trydint gum is greater than 0.3. The proportion of all people that prefer Trydint gum is 0.3 The average of people that prefer Trydint gum is 0.3. Based on a sample of 280 people, 58 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: Reject the null hypothesis Fail to reject the null hypothesis

Answer 1

Solution:

Given:

Claim:  3 out of 10 people prefer their gum to "Eklypse".

Part a) The null and alternative hypothesis in symbols would be:

H₀ : p = 0.3 Vs H₁ : p ≠ 0.3

Part b) The null hypothesis in words would be:

The proportion of all people that prefer Trydint gum is 0.3

Part c)

n = 280

x = 58

Thus sample proportion is:

Thus the point estimate is

Part d) The 99 % confidence interval is

where

Z_c is z critical value for c = 0.99 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.99 ) / 2 = 1.99 /2 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus Z_c = 2.575

Thus

Thus

Part e) Decision:

Since both limits of confidence interval are less than claimed proportion 0.3, we reject null hypothesis.