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In: Statistics and Probability

The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow...

The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county's residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area.

A researcher is hired to conduct a study to determine whether Smart County's residents have, on average, higher Full Scale IQs than the population. A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105. Use α=0.05α=0.05 level of significance.

  1. Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average?
    • z-test for the population mean
    • t-test for the population mean
    • z-test for the population proportion
    • t-test for the population proportion
  2. What are the null and alternative hypotheses?
    • H0: μ = 105; Ha: μ ≠ 105
    • H0: μ = 105; Ha: > 105
    • H0: μ = 105; Ha: μ ≠ 100
    • H0: μ = 100; Ha: > 100
  3. What is the value of the test statistic used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average?
    • .333
    • -.333
    • 3.33
    • -3.33
  4. After analyzing the data to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average, the P-value of .0004 was obtained.
    • Do not reject the null hypothesis. The average Full Scale IQ of Smart County residents is not higher than the population average.
    • Do not reject the null hypothesis. The average Full Scale IQ of Smart County residents is higher than the population average.
    • Reject the null hypothesis. The average Full Scale IQ of Smart County residents is not higher than the population average.
    • Reject the null hypothesis. The average Full Scale IQ of Smart County residents is higher than the population average.

Solutions

Expert Solution

i) z-test for the population mean

ans-> iv) Reject the null hypothesis. The average Full Scale IQ of Smart County residents is higher than the population average.

orchestra answered 2 years ago
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