You may need to use the appropriate appendix table or technology to answer this question. Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (14 of which defaulted) and 80 loans approved by Norm (9 of which defaulted). (a) State the hypothesis test that the default rates are the same for the two loan officers. (Let p1 = the population proportion of Carl's loans that default, and let p2 = the population proportion of Norm's loans that default. Enter != for ≠ as needed.) H0:       Ha:       (b) What is the sample default proportion for Carl?   What is the sample default proportion for Norm?   (c) Use a 0.05 level of significance. Calculate the test statistic. (Use  p1 − p2.  Round your answer to two decimal places.)   What is the p-value? (Round your answer to four decimal places.) p-value =  What is your conclusion? Reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.Do not reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.    Do not reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.Reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.

A recent report by PEW Research Center, published on February 25, 2022 summarizes American views on Russia threat as follows. “When it comes to rising U.S.- Russia tensions, an early January survey found that 26% of Americans considered the Russian military buildup near Ukraine to be a major threat to U.S. interests, while 33% said it was a minor threat to U.S. interests. Another 7% said it was no threat at all. A relatively large share of U.S. adults (33%) said they were not sure how Russian actions toward Ukraine affected U.S. interests.” Answer the questions based on the proportions listed above. (a) Use the binomial distribution to estimate the probability that more than half of 20 randomly selected US adults consider Russian military buildup near Ukraine to be a major or a minor threat to U.S. interests. (b) Use the normal approximation to estimate the probability that more than half of 20 randomly selected US adults consider Russian military buildup near Ukraine to be a major or…

A friend of yours tells you that they heard that 65% of all college athletes end up losing a finger or toe in their college athletic career.  You're highly skeptical of this, but your not sure if that percentage is an over exageration or an under exageration.  You survey 101 former student-athletes and find that 60 of them lost a digit during their college athletic career.  Is this enough evidence to conclude that the true percentage of student-athletes that lose a digit during their collegiate career is really different from 65%?

A loan officer compares the interest rates for 48-month fixed-rate auto loans and 48-month variable-rate auto loans. Two independent, random samples of auto loan rates are selected. A sample of five 48-month variable-rate auto loans had the following loan rates: 2.50% while a sample of five 48-month fixed-rate auto loans had loan rates as follows: 4.028% 3.93% 4.395% 3.65% Figure 11.7 JMP Output of Testing the Equality of Mean Loan Rates for Variable and Fixed 48-Month Auto Loans. Means and Std Deviations Level Fixed Variable 3.12% 2.880% 3.19% 3.22% t Test. Variable-Fixed Assuming equal variances Difference Std Err Dif Upper CL Dif Lower CL Dif Confidence HO: uf- uv = we will we will Number 5 5 t= -1.0586 0.1841 -0.6341 -1.4831 0.95 4.20% p-value= (a) Set up the null and alternative hypotheses needed to determine whether the mean rates for 48-month variable-rate and fixed-rate auto loans differ. Mean 4.04060 2.98200 t Ratio DF Prob > |t| Prob > t Prob < t (b) Figure 11.7 gives the JMP…