Testing For A Population Mean: Small Sample Standards

Question

Testing For A Population Mean Small Sample Population Standard Devia Testing for a Population Mean: Small Sample, Population Standard Deviation Unknown What do we do when the sample is less than 30 and the population standard deviation is not known? Use the Student t distribution with n – 1 degrees of freedom and a t test statistic. t = x̄ – μ / (s/√n) Example: p. 355, ex. 17 (Statistics for Business and Economics, Lind, Marchal, & Wathen, 15th ed., McGraw Hill Irwin). The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.4 liters. A health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign showed the following consumption in liters: 1.5, 1.6, 1.5, 1.4, 1.9, 1.4, 1.3, 1.9, 1.8, 1.7 At the 0.05 significance level, can we conclude that water consumption has increased beyond 1.4 liters? HA is the alternative hypothesis, and H0 is the null hypothesis. The claim made or concern expressed in the problem determines the sign in HA, and the opposite of that sign is placed in H0. Since the concern is water consumption increasing beyond 1.4 liters, this populates HA, resulting in HA: μ > 1.4. What is not in HA populates H0, so HO: μ ≤ 1.4. HO: μ ≤ 1.4 HA: μ > 1.4 α = 0.05 (the default significance level is 5% or 0.05 unless told otherwise in the problem) Sample data: 1.5, 1.6, 1.5, 1.4, 1.9, 1.4, 1.3, 1.9, 1.8, 1.7 Enter the data into the t calculator. Enter the test mean as 1.4 (the value being tested in H0 and HA). Click on Submit. t = 2.928 p = 0.0084; p-value is always the smaller of > 1.4 or α. Decision: Reject H0 since p (0.0084)

Dr. Jack HW Helper · Accepted Answer

Testing For A Population Mean Small Sample Population Standard Devia Testing for a Population Mean: Small Sample, Population Standard Deviation Unknown What do we do when the sample is less than 30 and the population standard deviation is not known? Use the Student t distribution with n – 1 degrees of freedom and a t test statistic. t = x̄ – μ / (s/√n) Example: p. 355, ex. 17 (Statistics for Business and Economics, Lind, Marchal, & Wathen, 15th ed., McGraw Hill Irwin). The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.4 liters. A health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign showed the following consumption in liters: 1.5, 1.6, 1.5, 1.4, 1.9, 1.4, 1.3, 1.9, 1.8, 1.7 At the 0.05 significance level, can we conclude that water consumption has increased beyond 1.4 liters? HA is the alternative hypothesis, and H0 is the null hypothesis. The claim made or concern expressed in the problem determines the sign in HA, and the opposite of that sign is placed in H0. Since the concern is water consumption increasing beyond 1.4 liters, this populates HA, resulting in HA: μ > 1.4. What is not in HA populates H0, so HO: μ ≤ 1.4. HO: μ ≤ 1.4 HA: μ > 1.4 α = 0.05 (the default significance level is 5% or 0.05 unless told otherwise in the problem) Sample data: 1.5, 1.6, 1.5, 1.4, 1.9, 1.4, 1.3, 1.9, 1.8, 1.7 Enter the data into the t calculator. Enter the test mean as 1.4 (the value being tested in H0 and HA). Click on Submit. t = 2.928 p = 0.0084; p-value is always the smaller of > 1.4 or α. Decision: Reject H0 since p (0.0084)

Testing For A Population Mean Small Sample Population Standard Devia

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