This exercise is a "what-if" analysis designed to determine what happens to the test statistics and interval estimates when elements of the statistical inference change. This problem can be solved manually, or using an Excel spreadsheet. In random samples of 12 from each of two normal populations, we found the following statistics: 71 = 78 $1 = 19 71 = 75 $1 = 18 ) Test with a = 0.05 to determine whether we can infer that the population means differ. State the null and alternative hypotheses. Ho : 141 - H2 # Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. There is not enough evidence to infer that the population means differ. (b) Repeat part (a) increasing the standard deviations to $1 = 208 and $2 = 193. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. There is not enough evidence to infer that the population means differ. (c) Describe what happens when the sample standard deviations get larger. When the sample standard deviations get larger the value of the test statistic decreases and the p-value |increases v ] O.(d) Repeat part (a) with samples of size 150. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. There is not enough evidence to infer that the population means differ. (e) Discuss the effects of increasing the sample size. When the sample size is increased the value of the test statistic increases v and the p-value decreases v (f) Repeat part (a) changing the mean of sample 1 to $1 = 80. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. There is not enough evidence to infer that the population means differ. (g) Discuss the effect of increasing @1- When #1 is increased the value of the test statistic increases |and the p-value decreases v O