Researchers measured the length of time people spend brushing their teeth. For the 154 subjects in their study, the mean was 72.8 seconds with a standard deviation of 23. 5 seconds. Use this information with a 0.10 significance level to test the claim that the mean teeth brushing time was less than 80 seconds. What is the test statistic for this problem?
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.
Given,
Sample size = 154
Sample mean = 72.8
Sample standard deviation = 23.5
Set up the null and the alternative hypothesis.
Critical value:
The critical value at the given level of significance with 153 degrees of freedom is, -1.287.
Decision rule:
Calculate test statistic:
The test statistic for one sample t test is,
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