Note that we never actually accept the null hypothesis, we just conclude that there isn’t enough evidence to reject it! We can safely reject the null hypothesis in favor of the alternative hypothesis - there’s enough evidence to suggest that the population mean for our class ratings is greater than 0.Ĭonversely, if the p-value is greater than the critical value, we fail to reject the null hypothesis and conclude that the mean rating is not greater than 0. That’s a good sign for us, because it means that our sample is unlikely under the null, and therefore the null is a poor explanation for the data.
If the p-value is smaller than our critical value of 0.05, that means that under the null hypothesis, the probability of observing a sample mean as high as we did by random chance is low. X̄ is the sample mean, μ is the population mean, s is the standard deviation, and n is the sample size. Let’s dive into the notebook look over the codes to compute and visualize the concepts explained above. In Python, the function is used to calculate a confidence interval for a normal distribution.
To calculate the margin of error, it is required to determine the confidence level that we want to find (for example, 95%), and determine the Z score that marks the threshold above or below which the values that are not within the chosen interval.
MEAN OF SAMPLING DISTRIBUTION OF XBAR PLUS
We know that the value of the mean weight and we assume this is also the population mean for all bags but how confident can we be that the true mean weight of all carry-on bags is close to the value?Ĭonfidence intervals are expressed as a sample statistic ± ( plus or minus) a margin of error. In a normal distribution, the z-score for 95% is 1.96 so our margin of error is -/+ 0.0466x1.96, which gives our confidence interval within which the mean will be in 95% of samples.įor example, our bag weight sampling distribution is based on samples of the weights of bags carried by passengers through our airport security line. For our variable, so we can use a table of z-scores to determine the number of standard deviations above and below the mean within which 95% of the data falls, and then multiply by the standard deviation for our distribution. The central limit theorem has resulted in a normal distribution.
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