Assume that the swim times for the 25-yard freestyle are normal.Ī college football coach thought that his players could bench press a mean weight of 275 pounds. Conduct a hypothesis test using a preset α = 0.05. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. For the 15 swims, Jeffrey’s mean time was 16 seconds. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims. His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster by using goggles. Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle, with a standard deviation of 0.8 seconds. Please provide more than just the answer. Solve Examples 1 and 2 using Minitab and interpret the output in each example to conclude whether the null hypothesis must be rejected. Model summary: Since the p-value is smaller than alpha level (0.05), we reject the null hypothesis and claim that average height of our basketball players is statistically different from 7 feet.***If you don’t have experience using Minitab software, please do not attempt the following 2 problems: The one-sample t-test result appears automatically in the session window.Enter the hypothesized value “7” into the box next to “Perform hypothesis test.”.Check the box of “Perform hypothesis test.”.Select “HtBk” as the “Samples in columns.”.Click the blank drop-down box and select “One or more samples, each in a column”.A new window named “One Samplet for the Mean” pops up.Click Stat → Basic Statistics → 1 Sample.Now we can run the one-sample t-test, knowing the data are normally distributed. If the data are not normally distributed, you need to use hypothesis tests other than the one sample t-test. Since the p-value of the normality is 0.275, which is greater than alpha level (0.05), we fail to reject the null and claim that the data are normally distributed. Alternative Hypothesis(H a): The data are not normally distributed.Null Hypothesis(H 0): The data are normally distributed.A new window named “Probability Plot of HtBk” appears, which covers the results of the normality test.A new window named “Normality Test” pops up.Click Stat → Basic Statistics → Normality Test.Step 1: Test whether the data are normally distributed Data File: “One Sample T-Test” tab in “Sample Data.xlsx” Use Minitab to Run a One-Sample T-TestĬase study: We want to compare the average height of basketball players against 7 feet. If |tcalc| < tcrit, we fail to reject the null and claim there is not any statistically significant difference between the population mean μ and the specified value μ0. One sample t-test is more robust than the z-test when the sample size is small ( tcrit, we reject the null and claim there is a statistically significant difference between the population mean μ and the specified value μ0.The variance of the population of our interest is unknown.The data of the population are normally distributed.
Hypothesis tests help to determine whether a hypothesis about a population or multiple populations is true with certain confidence level based on sample data. A hypothesis test is a statistical method in which a specific hypothesis is formulated about a population, and the decision of whether to reject the hypothesis is made based on sample data. We apply a one sample t test when the population variance (σ) is unknown and we use the sample standard deviation (s) instead. In statistics, a t test is a hypothesis test in which the test statistic follows a Student’s t distribution if the null hypothesis is true.