We fail to reject the null hypothesis and conclude that there is not enough evidence to say that there is a difference in the mean time it takes to open the two locks.
A paired samples t-test would be the most appropriate hypothesis test for this analysis. This is because the students were each given the combination to both locks, so the data is paired. The paired samples t-test is used to compare the means of two paired groups.
Here are the steps for conducting a paired samples t-test:
State the null and alternative hypotheses.
Null hypothesis: There is no difference in the mean time it takes to open the two locks.
Alternative hypothesis: There is a difference in the mean time it takes to open the two locks.
Calculate the t-statistic.
The t-statistic is a measure of how many standard deviations the difference between the two sample means is from zero.
Calculate the p-value.
The p-value is the probability of getting a t-statistic as extreme or more extreme than the one calculated, assuming that the null hypothesis is true.
Make a decision.
If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant difference in the mean time it takes to open the two locks. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to say that there is a difference in the mean time it takes to open the two locks.
In this case, the p-value is 0.102, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to say that there is a difference in the mean time it takes to open the two locks.