erage American consumes 84 liters of alcohol per year. Does the average college student consume less alcohol per year? A researcher surveyed 14 randomly selected college students and found that they averaged 74.4 liters of alcohol consum
erage American consumes 84 liters of alcohol per year. Does the average college student consume less alcohol per year? A researcher surveyed 14 randomly selected college students and found that they averaged 74.4 liters of alcohol consum
erage American consumes 84 liters of alcohol per year. Does the average college student consume less alcohol per year? A researcher surveyed 14 randomly selected college students and found that they averaged 74.4 liters of alcohol consum
The average American consumes 84 liters of alcohol per year. Does the average college student consume less alcohol per year? A researcher surveyed 14 randomly selected college students and found that they averaged 74.4 liters of alcohol consumed per year with a standard deviation of 21 liters. What can be concluded at the the αα = 0.01 level of significance?
H0:
H1:
The test statistic:
The p-value =
he p-value is ? a
Based on this, we should Select an answer accept fail to reject reject the null hypothesis.
Thus, the final conclusion is that ...
The data suggest the populaton mean is significantly less than 84 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed by college students is less than 84 liters per year.
The data suggest that the population mean amount of alcohol consumed by college students is not significantly less than 84 liters per year at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is less than 84 liters per year.
The data suggest the population mean is not significantly less than 84 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is equal to 84 liters per year.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
Step 1
The null and alternative hypotheses are:
Ho: μ = 84
H1: μ < 84
This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation, will be used.
The t-statistic is computed as follows:
The p-value with 13(n-1) degrees of freedom and left tailed test is p=0.0555 (from t distribution table), and since p=0.0555≥0.01, it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean μ is less than 84, at the 0.01 significance level.
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