This has me puzzled. I am doing a right sided t-test where the null hypothesis is rejected based on the critical t value and the p value but the sample confidence interval includes the expected value. There is something missing in my understanding because I thought if the confidence interval included the value you could conclude there is no difference between the sample and hypothesized value.
The null hypothesis is rejected for the following reasons:
Reject the null hypothesis because the t-statistic, 1.54, was greater than the critical t value, 1.383.
Reject the null hypothesis because the p-value, 0.079, was less than the significance level, 0.1.
Here are the values used in the calculation:
Ho: mean <= 50.5 Ha: mean > 50.5 Expected Mean: 50.5 Sample Mean: 53.7 Sample Standard Deviation: 6.567 Standard Error: 2.077 Sample Size: 10 Significance Level: .1 Sample 90% Confidence Interval: [49.89, 57.51] p-Value: .079 t-Statistic: 1.54 Cohen's D: .49 Critical T: 1.383
Do any of you know why this is happening?