For a single sample t-test we don't need to know.................of the population, instead we will have access to the ............of the sample.
For a single sample t-test, we don't need to know the parameters (mean and standard deviation) of the population, instead we will have access to the statistics (mean and standard deviation) of the sample.
To perform a single sample t-test, we typically start with a hypothesis about the population mean and then collect a sample from the population. The sample should be randomly selected and representative of the population of interest.
Once we have the sample, we calculate the sample mean (x̄) and the sample standard deviation (s) using the data. Then, we compare the sample mean to the hypothesized population mean using a t-test.
The t-test specifically examines whether the difference between the sample mean and the hypothesized population mean is statistically significant. In other words, it helps us determine if the sample mean is significantly different from what we originally assumed about the population mean.
By comparing the sample mean and the hypothesized population mean, along with the sample standard deviation, we can calculate the t-value. The t-value measures the difference between the sample mean and the population mean in terms of standard errors.
Finally, we use the t-value to calculate the p-value, which represents the probability of observing the sample mean if the null hypothesis (no difference between the sample mean and the population mean) is true. If the p-value is below a predetermined significance level (usually 0.05), we reject the null hypothesis and conclude that there is a statistically significant difference between the sample mean and the population mean.
To summarize, in a single sample t-test, knowing the parameters of the population is not necessary. Instead, we use the statistics (mean and standard deviation) of the sample to compare and make inferences about the population mean.