A simple random sample of 30 filtered 100-mm cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.22 mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below. a. What are the null and alternative hypotheses? A. H0: σ>0.35 mg H1: σ≤0.35 mg B. H0: σ=0.35 mg H1: σ<0.35 mg C. H0: σ=0.35 mg H1: σ≠0.35 mg D. H0: σ≠0.35 mg H1: σ=0.35 mg b. Find the test statistic. χ2= c. Find the P-value of the test statistic. The P-value of the test statistic is d. State the conclusion. Fail to reject Reject H0. There is is not sufficient evidence to conclude that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35 mg.
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.
mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35
mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below.
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