Question

A scientist claims that pneumonia causes weight loss in mice. The table shows the weights​ (in grams) of six mice before infection and two days after infection. At alphaequals0.10​, is there enough evidence to support the​ scientist's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below. Mouse 1 2 3 4 5 6 Weight​ (before) 20.3 23.6 21.3 19.8 23.3 22.4 Weight​ (after) 20.1 23.7 21.2 19.8 23.3 22.3 (a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa. What is the​ claim? A. Pneumonia causes weight gain in mice. B. Weight gain causes pneumonia in mice. C. Pneumonia causes weight loss in mice. Your answer is correct. D. Weight loss causes pneumonia in mice. Let mu Subscript dμd be the hypothesized mean of the difference in the weights ​(beforeminus−​after). What are Upper H 0H0 and Upper H Subscript aHa​? A. Upper H 0H0​: mu Subscript dμdgreater than or equals≥0 Upper H Subscript aHa​: mu Subscript dμdless than<0 B. Upper H 0H0​: mu Subscript dμdless than or equals≤d overbard Upper H Subscript aHa​: mu Subscript dμdgreater than>d overbard C. Upper H 0H0​: mu Subscript dμdequals=0 Upper H Subscript aHa​: mu Subscript dμdnot equals≠0 D. Upper H 0H0​: mu Subscript dμdless than or equals≤0 Upper H Subscript aHa​: mu Subscript dμdgreater than>0 Your answer is correct. E. Upper H 0H0​: mu Subscript dμdnot equals≠0 Upper H Subscript aHa​: mu Subscript dμdequals=0 F. Upper H 0H0​: mu Subscript dμdgreater than or equals≥d overbard Upper H Subscript aHa​: mu Subscript dμdless than Your answer is not correct. B. tless thannothing C. tless than

Answer 1

Answer 2

(a) The claim is "Pneumonia causes weight loss in mice." Upper H0: μd = 0 (There is no significant difference in weight before and after pneumonia infection.) Upper Ha: μd < 0 (Weight loss occurs after pneumonia infection.)

(b) Upper H0: μd ≤ 0 (There is no significant weight loss after pneumonia infection or weight gain may occur.) Upper Ha: μd < 0 (Weight loss occurs after pneumonia infection.)

(c) The correct answer is (b).

(d) Using a one-tailed t-test with α = 0.10 and 5 degrees of freedom, the critical t-value is -1.476. The test statistic is calculated as:

t = (d̄ - μd) / (s / √n) where d̄ is the sample mean of the differences, μd is the hypothesized mean of the differences (μd = 0), s is the sample standard deviation of the differences, and n is the sample size (n = 6 in this case).

The sample mean of the differences is:

d̄ = (20.3 - 20.1) + (23.6 - 23.7) + (21.3 - 21.2) + (19.8 - 19.8) + (23.3 - 23.3) + (22.4 - 22.3) / 6 = -0.0333

The sample standard deviation of the differences is:

s = sqrt(((20.3 - 20.1 - d̄)² + (23.6 - 23.7 - d̄)² + (21.3 - 21.2 - d̄)² + (19.8 - 19.8 - d̄)² + (23.3 - 23.3 - d̄)² + (22.4 - 22.3 - d̄)²) / (6 - 1)) = 0.1863

Substituting the values into the t-test formula, we get:

t = (-0.0333 - 0) / (0.1863 / √6) = -0.5989

Since the test statistic (-0.5989) is greater than the critical t-value (-1.476), we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the scientist's claim that pneumonia causes weight loss in mice at α = 0.10.