Coronary heart disease (CHD) begins in young adulthood and is the fifth leading cause of death among adults aged 20 to 24 years. Studies of serum cholesterol levels among college students, however, are very limited. A 1999 study looked at a large sample of students from a large southeastern university and reported that the mean serum cholesterol level among women is 168 mg/dl with standard deviation of 27 mg/dl. The initial research was conducted to give a test of a hypothesis about the cholesterol level for female sedentary undergraduates based on a sample of size n = 71. The hypotheses are H0: μ = 168 Ha: μ ≠ 168 While the result was not statistically significant, it did provide some evidence that the mean was larger than 168. Thus, the researcher plans to recruit another sample of sedentary females but this time using a one-sided alternative. He plans to obtain n = 70 subjects and wonders if this sample size give him adequate power to detect an increase of 5 mg/dl to μ = 173.  Given ? = 0.05, for what values of z will he reject the null hypothesis?  Using ? = 27 and ? = 168, for what values of ?̅ will he reject H0?  Using ? = 27 and ? = 173, what is the probability ?̅ will fall in the region defined in part (b)?

Question
  1. Coronary heart disease (CHD) begins in young adulthood and is the fifth leading cause of death among adults aged 20 to 24 years. Studies of serum cholesterol levels among college students, however, are very limited. A 1999 study looked at a large sample of students from a large southeastern university and reported that the mean serum cholesterol level among women is 168 mg/dl with standard deviation of 27 mg/dl. The initial research was conducted to give a test of a hypothesis about the cholesterol level for female sedentary undergraduates based on a sample of size n = 71. The hypotheses are

    H0: μ = 168 Ha: μ ≠ 168

    While the result was not statistically significant, it did provide some evidence that the mean was larger than 168. Thus, the researcher plans to recruit another sample of sedentary females but this time using a one-sided alternative. He plans to obtain n = 70 subjects and wonders if this sample size give him adequate power to detect an increase of 5 mg/dl to μ = 173. 

    1. Given ? = 0.05, for what values of z will he reject the null hypothesis? 

    2. Using ? = 27 and ? = 168, for what values of ?̅ will he reject H0? 

    3. Using ? = 27 and ? = 173, what is the probability ?̅ will fall in the region defined in part (b)? 

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