Question

"Trydint" bubble-gum company claims that 5 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:

• H0:μ≤0.5
  H1:μ>0.5
• H0:p=0.5
  H1:p≠0.5
• H0:μ≥0.5
  H1:μ<0.5
• H0:p≤0.5
  H1:p>0.5
• H0:μ=0.5
  H1:μ≠0.5
• H0:p≥0.5
  H1:p<0.5

The null hypothesis in words would be:

• The proportion of all people that prefer Trydint gum is less than 0.5.
• The proportion of all people that prefer Trydint gum is 0.5
• The proportion of people in a sample that prefers Trydint gum is 0.5.
• The average of people that prefer Trydint gum is not 0.5.
• The proportion of all people that prefer Trydint gum is greater than 0.5.
• The average of people that prefer Trydint gum is 0.5.
• The proportion of people in a sample that prefer Trydint gum is not 0.5

Based on a sample of 100 people, 39 said they prefer "Trydint" gum to "Eklypse".

The point estimate is:  (to 3 decimals)

The 90 % confidence interval is:  to  (to 3 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Please explain how to solve on a TI-84 calculator. Thank you!!!

Answer 1

answer)

Null hypothesis Ho : P = 0.5

Alternate hypothesis Ha : P is not equal to 0.5

Null hypothesis in words:

• The proportion of all people that prefer Trydint gum is 0.5

Point estimate = 39/100 = 0.39

N = 100

P = 0.39

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 39

N*(1-p) = 61

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z for 90% confidence level is 1.645 (from z table)

Margin of error = 1.645*√p*(1-p)/√n

P = 0.39

N = 100

MOE = 0.08023486446

Confidence interval is given by

(P-MOE, P+MOE)

(0.30976513553, 0.47023486446)

(0.310, 0.470)

As the confidence interval does not contain the null hypothesized value 0.5

We reject the null hypothesis

Now:

To estimate the population proportion on ti-84

Press stat and scroll right to the TESTS menu

Then scroll down to 1 - PropZInt and press enter

Now enter the value

X = number of successes which is 39 here in this case

N = number of trials = 100 in this case

Then enter the c-level(confidence level) = 0.90 in this case

Then press calculate and enter