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Hypothesis Testing, Null and Alternate Hypothesis and Two-Tailed Hypothesis Tests

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5) ESPN reported in sample of 1000 homes the proportion of people who watched the Texas v. Ohio State college football game this weekend was .6. ESPN also reported that in another sample of 1000 homes the proportion of people who watched the Arizona State v. Louisiana State game was .4. Conduct a hypothesis test to determine if the proportion of people who watched the Texas v. Ohio State game was greater than the proportion of people who watched the Arizona State v. Louisiana State game ( ). Assume α = .03 and remember to clearly state both the null and alternate hypothesis and your conclusion about the proportion of people watching the two games.

6) Historically, Yosemite Toads lay about 25,000 eggs out of which 15,000 typically hatch (60%). Yosemite National Park Rangers have been monitoring the amount of eggs hatching from Yosemite Toad egg bundles. Recently, Yosemite Rangers took a sample of 100 egg bundles and found that 45% of the eggs hatched. The Rangers would like to know if the true proportion of Yosemite Toad eggs that hatch is really 60% or some other proportion ( ). Conduct a two-tailed hypothesis test to determine if the true proportion of eggs hatching is 60% or not. Assume α = .01 and remember to clearly state both the null and alternate hypothesis as well as your conclusion about the proportion of Yosemite Toad eggs that hatch.

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Hypothesis Testing, Null and Alternate Hypothesis and Two-Tailed Hypothesis Tests are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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