(a) What is the level of significance? State the null and alternate hypotheses. Will do you use a left-tailed, right-tailed, or two-tailed test? (b) What sampling distribution will you use? Explain the rationale for your choice of the sampling distribution. What is the value of the sample test statistic? (c) Find (or estimate) the P-value. Sketch the sampling distribution and show the the area corresponding to the P-value.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
(a) What is the level of significance? State the null and alternate hypotheses. Will do you use a left-tailed, right-tailed, or two-tailed test?
(b) What sampling distribution will you use? Explain the rationale for your choice of the sampling distribution. What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
(e) State your conclusion in the context of the application.
Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is hypothesized that regular exercise might help reduce headaches. If a random sample of 210 patients using diltiazem exercised regularly, and only 16 had a headache, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance.
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