9.6-One Sample Hypothesis Testing-handwritten pdf upload required. For this homework assignment, perform the hypothesis test for the following 4 problems by hand. For proportion problems, always use z test and for mean problems, use z if is known and t test if is unknown. Submit a handwritten pdf. Label each problem correctly. For each problem, do the following in given order. State if it is a mean problem or proportion problem. Clearly state the null and alternative hypothesis. Label the claim. Include formula for test statistic, correctly labeled test statistic, critical value/s. State your decision and conclusion in complete sentence including context of the problem. Now find the P value for this problem and verify that you have correct decision and conclusion. Show all work in vertical format. Not providing all of the above steps for each of the following problems will result in a score of zero for this assignment. #1 A bus company advertised a mean time of 150 minutes for a trip between two cities. A consumer group had reason to believe that the mean time was more than 150 minutes. A sample of 40 trips showed a mean x= 153 minutes and a standard deviation s=7.5 minutes. At the .05 level of significance, test the consumer group's belief. #2 A bank claims that the mean wait time during lunch hour is 6 min. To test the claim they took a random sample of 28 people during lunch time and found that the mean wait time is 6.8 min with a standard deviation of 1.82 min. Test bank's claim at =0.05 . Assume that the wait time follows normal distribution. #3 The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 lb. Assuming that population standard deviation is known to be 121.8 lb, use a 0.01 significance level to test claim that the population mean of all such bear weights is less than 200lb. #4 Mr. Clean claims that at least 60% of female car owners have a hybrid car. In a random sample of 100 female car owners, 58 owned a hybrid car. Is there enough evidence to support Mr. Clean's claim? Use =.05