Question

In: Statistics and Probability

An auditor takes two independent samples - a random sample of 150 small businesses and a...

An auditor takes two independent samples - a random sample of 150 small businesses and a random sample of 100 medium-sized businesses. She finds that 27 small businesses and 12 medium-sized businesses are under financial distress. Answer the following questions using (1) formulae and (2) Excel.

  1. Construct a 95% CI for the difference in the two (population) proportions of businesses which have financial distress.   
  2. Test, at the 5% level of significance, whether the (population) proportion of the small businesses that are under financial distress is at one least 2% higher than that of the medium-sided businesses.   

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Two random samples are selected from two independent populations. A summary of the samples sizes, sample...
Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: n1=37,n2=44,x¯1=58.9,x¯2=74.7,s1=5.5s2=10.1 n 1 =37, x ¯ 1 =58.9, s 1 =5.5 n 2 =44, x ¯ 2 =74.7, s 2 =10.1 Find a 95.5% confidence interval for the difference μ1−μ2 μ 1 − μ 2 of the means, assuming equal population variances. Confidence Interval
Two random samples are selected from two independent populations. A summary of the samples sizes, sample...
Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: n1=39,n2=48,x¯1=52.5,x¯2=77.5,s1=5s2=11 Find a 97.5% confidence interval for the difference μ1−μ2 of the means, assuming equal population variances. Confidence Interval =
Two random samples are selected from two independent populations. A summary of the sample sizes, sample...
Two random samples are selected from two independent populations. A summary of the sample sizes, sample means, and sample standard deviations is given below: n1=43, x¯1=59.1, ,s1=5.9 n2=40, x¯2=72.6, s2=11 Find a 99% confidence interval for the difference μ1−μ2 of the means, assuming equal population variances. _________<μ1−μ2<____________
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n1 = 50 n2 = 30 x1 = 13.4 x2 = 11.7 σ1 = 2.3 σ2 = 3 What is the point estimate of the difference between the two population means? Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). ( , ) Provide a 95% confidence interval for the difference between the two population means...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 1 = 50 n 2 = 35 x 1 = 13.1 x 2 = 11.5 σ 1 = 2.4 σ 2 = 3.2 What is the point estimate of the difference between the two population means? (to 1 decimal) Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( ,  ) Provide a 95%...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 1 = 50 n 2 = 35 x 1 = 13.6 x 2 = 11.1 σ 1 = 2.4 σ 2 = 3.4 What is the point estimate of the difference between the two population means? (to 1 decimal) Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Provide a 95% confidence interval for the...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 1 = 40 n 2 = 30 x 1 = 13.1 x 2 = 11.1 σ 1 = 2.3 σ 2 = 3.4 What is the point estimate of the difference between the two population means? (to 1 decimal) Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( ,  ) Provide a 95%...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 1 = 50 n 2 = 30 x 1 = 13.8 x 2 = 11.5 σ 1 = 2.4 σ 2 = 3.4 What is the point estimate of the difference between the two population means? (to 1 decimal) Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( , ) Provide a...
The following results come from two independent random samples taken of two populations. Sample 1 Sample...
The following results come from two independent random samples taken of two populations. Sample 1 Sample 2 n1 = 60 n2 = 35 x1 = 13.6 x2 = 11.6 σ1 = 2.5 σ2 = 3 (a) What is the point estimate of the difference between the two population means? (Use x1 − x2.) (b) Provide a 90% confidence interval for the difference between the two population means. (Use x1 − x2. Round your answers to two decimal places.)   to   (c)...
You are given two independent random samples from two populations. For Sample #1, there are 60...
You are given two independent random samples from two populations. For Sample #1, there are 60 observations, the sample mean is 33.8 and you are given that the populationstandard deviation is 5.5 For Sample #2, there are 35 observations, the sample mean is 31.8 and you are given that the populationstandard deviation is 4.1 You are asked to test the null hypothesis that the two population have the same mean (the difference in population means is 0). What is the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT