I am having trouble with section of two proportions and two means independent sample.

Math 150, Spring 2021 El Camino College G. Song Chapter 9: Worksheet Section 9.1: Two Proportions 1: A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 291 vinyl gloves, 56 of them leaked viruses. Among 291 latex gloves, 32 of them leaked viruses. Using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. test statistic = 2.776949126, p-value = 0.00027436465 2: Among 2079 passenger cars in a particular region, 240 had only rear license plates. Among 384 commercial trucks, 54 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.05 significance level to test that hypothesis. Identify the null and alternative hypothesis, test statistics, P-value, and state the final conclusion that addresses the original claim. test statistic = -1.398497151, p-value = 0.080981966 3: A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 313 people over the age of 55, 68 dream in black and white, and among 314 people under the age of 25, 19 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. test statistic = 5.676778827, p-value = 6.8821893E -9 1: Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 22 having a common attribute. The second sample consists of 2000 people with 1406 of the having the same common attribute. Use a 0.01 significance level to test the claim that the two populations has the same proportion with a common attribute. test statistic = -2.090796157, p-value = 0.0365462124Math 150, SE' 5 2021 El Caminu College G. Sung Section 9.2: Two Means: Independent Samples 5: Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized as followed: m = 32, '1 = 0.79375, 31 = 0.00446, M = 32, 2 = 0.80569, 32 = 0.00752 Assume that the two samples are independent simple random samples selected from normallg,r distributed populations, and do not assume that the population standard devi ations are equal. Use a 0.05 signicance level to test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. test statistic = 7.725283388, pvalue = 2.1065E 10 6: A study was done on proctored and nonproctored tests. The results are shown below: m = 31, i1 = 77.16, .51 = 10.98, M = 35, 2 = 81.91, a; = 19.38 Assume that the two samples are independent simple random samples selected from normallg,r distributed populations, and do not assume that the population standard de viations are equal. Use a 0.01 signicance level to test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. test statistic = 1.242280039, pvalue = 01097053041 7: Listed below are student evaluation scores of female professors and male professors: Females: 4.4, 3.4, 3.8, 2.9, 4.4, 4.1, 3.5, 3.7, 3.4, 4.8 Males: 4.0, 4.6, 4.1, 4.1, 4.5, 4.6, 4.0, 4.3, 4.5, 4.3 Use 0.05 signicance level to test the claim that female professors and male professors have the same mean evaluation ratings. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. test statistic = 2.318100335, pvalue 2 00388904571