Answer:
The correct answer is B. With a t statistic of 1.4789 and P-value of 0.173292, fail to reject the null hypothesis that prices have not changed.
Step-by-step explanation:
To determine whether there has been a significant change in prices, we need to perform a two-sample t-test with the null hypothesis that the mean difference between before and after prices is zero.
We can calculate the sample mean and standard deviation of the difference in prices as follows:
Mean difference = (0.30 - 0.31 + 0.26 + 0.04 + 0.06 + 0.14 - 0.09 - 0.02 - 0.04 + 0.07) / 10 = 0.022
Standard deviation = sqrt([sum of (differences - mean difference)^2] / (n - 1)) = sqrt((0.09 + 0.0961 + 0.0004 + 0.0016 + 0.0036 + 0.0196 + 0.0081 + 0.0004 + 0.0016 + 0.0049) / 9) = 0.112
where 'differences' are the differences between the before and after prices and 'n' is the sample size (which is 10 in this case).
Using these values, we can calculate the t statistic as:
t = (mean difference - 0) / (standard deviation / sqrt(n)) = 0.022 / (0.112 / sqrt(10)) = 1.4789
where 0 is the null hypothesis mean (i.e., no change in prices).
To determine the P-value, we need to use a two-tailed t-test with 9 degrees of freedom (n - 1). From a t-table with 9 degrees of freedom and a significance level of 0.05, the critical values are -2.306 and 2.306.
Since the calculated t statistic (1.4789) falls within this range, we fail to reject the null hypothesis that the mean difference between before and after prices is zero. This means that there is not enough evidence to suggest that the new owner has significantly changed the prices.
Therefore, the correct answer is B. With a t statistic of 1.4789 and P-value of 0.173292, fail to reject the null hypothesis that prices have not changed.
Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]