Question

"Trydint' bubble-gum company claims that 3 out of 10 people prefer their gum to "Eklypse". The null and alternative hypothesis in symbols would be: OH: <0.3 H: > 0.3 OH:P < 0.3 H:p > 0.3 OH = 0.3 H:H70.3 Ho:p > 0.3 H:p < 0.3 OH: > 0.3 Hu<0.3 OH,:= 0.3 H:P +0.3 The null hypothesis in words would be: The proportion of people in a sample that prefer Trydint gum is not 0.3 The average of people that prefer Trydint gum is 0.3. The proportion of all people that prefer Trydint gum is 0.3 The average of people that prefer Trydint gum is not 0.3. The proportion of people in a sample that prefers Trydint gum is 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 less than 0.3. Based on a sample of 450 people, 113 said they prefer "Trydint' gum to "Eklypse". The point estimate is: (to 3 decimals)

Answer 1

Tridint bubble gum company claims that 3 out of 10 people prefer their gum to Eklypse,They are going to test whether proportion of people who prefer Tridint gum is 0.3 or not.

(a)So Null and Alternate hypothesis in symbol would be,

Ho : p = 0.3 [Claim]

Ha : p ≠ 0.3

1.So 6th option is correct

(b) Null hypothesis in words would be

The proportion of all people that prefer Tridint gum is 0.3

2.So 3rd option is correct

(c)Based on a sample of 450 people , 113 said the prefer tridint gum over eklypse.

So point estimate here will be sample proportion

113 p= = 0.251 n 450

3.The point estimate is 0.251.

(d)We need to construct the 95% confidence interval for the population proportion.

The critical value for α = 0.05 is

zc​(lower) = - 1.96 using excel formula =NORM.S.INV(0.025)

zc​(upper) =   1.96 using excel formula =NORM.S.INV(0.975)

But we use absolute value of zc = 1.96

$CI = \left ( p - z_{c}\sqrt{\frac{p(1-p)}{n}},p + z_{c}\sqrt{\frac{p(1-p)}{n}} \right )$

$CI = \left ( 0.251 - 1.96\sqrt{\frac{0.251(1-0.251)}{450}},0.251 + 1.96\sqrt{\frac{0.251(1-0.251)}{450}} \right )$$CI = \left ( 0.251 - 0.040,0.251 + 0.040 \right )$

$CI = \left ( 0.211 ,0.291 \right )$

The 95% confidence interval for the population proportion is 0.211<p<0.291, which indicates that we are %95% confident that the true population proportion  is contained by the interval (0.211, 0.291).

So based on this we can conclude proportion is not equal to 0.3 and null hypothesis is rejected.

4.So, reject the Null hypothesis