Business statistics

Question

Trydint" bubble-gum company claims that 9 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:

1. H0:μ≤0.9H0:μ≤0.9
2. H1:μ>0.9H1:μ>0.9

1. H0:μ=0.9H0:μ=0.9
2. H1:μ≠0.9H1:μ≠0.9

1. H0:p≥0.9H0:p≥0.9
2. H1:p<0.9H1:p<0.9

1. H0:p=0.9H0:p=0.9
2. H1:p≠0.9H1:p≠0.9

1. H0:p≤0.9H0:p≤0.9
2. H1:p>0.9H1:p>0.9

1. H0:μ≥0.9H0:μ≥0.9
2. H1:μ<0.9H1:μ<0.9

1. The null hypothesis in words would be: Pick one
2. The proportion of people in a sample that prefer Trydint gum is not 0.9
3. The average of people that prefer Trydint gum is 0.9.
4. The proportion of people in a sample that prefers Trydint gum is 0.9.
5. The average of people that prefer Trydint gum is not 0.9.
6. The proportion of all people that prefer Trydint gum is greater than 0.9.
7. The proportion of all people that prefer Trydint gum is 0.9
8. The proportion of all people that prefer Trydint gum is less than 0.9.

Based on a sample of 400 people, 336 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:

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

Answer 1

Hello Salma,

(a) You were not told to measure greater than or less than, so that means, right away, that your null hypothesis will have "equal to" and your alternative will have "not equal to." You are also asked specifically about a proportion, not a mean, which means "p." Only answer that meets these criteria is:

1. H0:p=0.9H0:p=0.9
2. H1:p≠0.9H1:p≠0.9

(b) Null hypothesis means nothing--as in no difference from the claim. So that means we are claiming that something will equal 0.9. Now, we usually make hypotheses only about populations; we can typically get exact values for samples. Finally, we are still working with proportions, not means. So, only answer that makes sense is:

1. The proportion of all people that prefer Trydint gum is 0.9

(c) Point estimate is essentially that--an estimate at that exact point. Here, the proportion is:

336/400=0.840

(d) 400 is a large enough sample to apply the Central Limit Theorem and assume normality. With that in mind, formula for this confidence interval is:

CI=p-hat +/- z*(sqrt(p-hat(1-p-hat))/n)

Breaking this down:

p-hat=point estimate

z*=1.96, likely worth memorizing for 95% confidence if you haven't already

n=sample size

Thus:

p-hat=0.840

z*=1.96

n=400

CI=0.840 +/- 1.96*sqrt((0.840*0.160)/400)

CI=0.840 +/- 0.072

CI=(0.768, 0.912)

(e) Null hypothesis was: p=0.9. Do you see 0.9 in the confidence interval? Yes. It's near the top, but present. Therefore, we cannot reject the null. We conclude that 0.9 is a plausible value for true population proportion.

I hope this helps.