(b) Interpret a Type I error in terms of the problem. (c) Interpret a Type II error in terms of the problem. (d) If we wanted to minimize the probability of a Type I error, what action should we take? (e) If we wanted to minimize the probability of a Type II error, what action should we take?Book Homework 1. A medical researcher wishes to see whether the pulse rates of smokers are higher than the pulse rate for non- smokers. Random samples of (i5 smokers and 74 non- smokers are selected, and the pulse rate results are shown below. Test the researchers claim at (r = 0.01. Assume the (if. = 137. Smokers Nonsmokers Sample Mean 90 88 Sample Standard Deviation 5.9 7.3 Sample Size 65 7'4 (a) State the null hypothesis and the alternative hypoth esis. (1)) Calculate the teststatistic for this problem. (c) Calculate the range of the pvalue for your test statistic. (d) Interpret the p-value in terlns of the probleln. (e) Do you reject the null, or fail to reject? (f) State the conclusion in terms of the problem. 2. A scientist recorded the tail lengths (in cm) of two va- rieties of woodland salamanders: mud-hacked and lead- hacked. The table below shows the summary: Redhacked Leadhaeked Sample Mean 3.2 4.0 Sample Standard Deviation (1.9 (1.7 Sample Size 6'0 2? Assume the (if = 63.5677. The researcl'lers are inter ested in if the average tail lengths of the two salal'nal'lders are equal. (a) State the null hypothesis and the alternative hypoth esis. (1)) Calculate the teststatistic for this problem. (c) Calculate the range of the pvalue for your test statistic. (d) Interpret the p-vall 1e in terms of the problem. (1'. { '.) Do you reject the null, or fail to reject? 0 State the conclusion in terms of the problem. 3. Consider the following research topic: The goal is to de- termine if there is a statistically significant increase in the average Weight gain of anorexic patients for a new treatment (pm) when compared to a standard treatment (#3)- (a) State the null hypothesis and the alternative hypoth esis