Question

28. The table shows the number of happy baseball fans in sample of Dodger fans and in a sample of Yankee fans. Assume that you plan to use a significance level of a = 0.05 to test the claim that the proportion of happy Dodger fans is higher than the proportion of happy Yankee fans. Given: Zerk = -5.87, Dodger fans are pl, Yankee fans are p2 Dodger fons (p12 Yankee fons (p2) Number in sample 155 124 Number satisfied with their pet 106 81 Use the 8-step process to test the claim. a. Identify, nt nz X1 X2 Calculate the pooled estimate, p b. Identify the claim c. Identify the opposite. d. State the null hypothesis (Hel. e. State the alternative hypothesis (H) f. Find the critical value and make a sketch. 9. Compare some to the critical value and state your verdict. h. Use the flow chart to state a conclusion Extra Credit 1 Are the requirements met to test a hypothesis for the following two population proportions? If not, state which requirement is not met, and show why it fails. In a random sample of 150 car owners, 82% said they were happy with the fuel economy their car. In a random sample of 85 truck owners, 3% said they were happy with they fuel economy of their truck Extra Credit 12 1 Are the following independent or dependent samples? A study titled "How much Solt on the Fries?" examined the amount of sodium on 15 orders of fries from McDonalds and 18 orders of fries from Wendy's Extra Credit #3 A Youtube ad claims that shoppers make online purchases on the four days of the long Thanksgiving weekend with the same frequency. Thurs Sat S Day Number of Online purchases 14 5 a. Identify the claim b. Identify the opposite c. State the null hypothesis MacBook Air 30 %

Answer 1

28.

a. $n_{1}=155,n_{2}=124,x_{1}=81,x_{2}=106$ ,

Pooled estimate of $\bar{p}=\frac{x_{1}+x_{2}}{n_{1}+n_{2}}=\frac{81+106}{155+124}=\frac{187}{279}=0.6703$

b. The claim: The proportion of the happy Dodger's fans is higher than the proportion of Yankee fans.

c. The opposite: The proportion of the happy Dodger's fans is same as the proportion of Yankee fans

d. Null hypothesis:

Ho: P1 = P2

e. Alternate Hypothesis: $H_{1}:p_{1}>p_{2}$

f. The critical value is Zc=1.6449

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g. Since the calculated value -5.87<the critical value, we fail to reject the null hypothesis.

h. Since, the null hypothesis is not rejected, we conclude that there is not sufficient evidence in the claim the proportion of the happy Dodger's fans is higher than the proportion of Yankee fans.

Extra credit #1.

Here, the proportion p=0.82, n=150, n.p(1-p)=22.14>10, the requirement is met.

In the next case, p=0.03, n=85,n.p(1-p)=24.735>10, the requirements are met.

Extra credit #2:

These are two independent samples since the sources are different.(Wendy's and McDonald)

Extra credit #3

a. The claim: The number of online purchases made on the 4 days of Thanksgiving weekend is different

b. The opposite: The number of purchases made on the 4 days are the same

c. $H_{0}:p_{1}=p_{2}=p_{3}=p_{4}$ where the p's indicate the proportion of online purchases are the same.