# Answer in Statistics and Probability for Kanwal #231427

To compare customer satisfaction levels of two competing ice cream companies, 8 customers of Company 1 and 5 customers of Company 2 were randomly selected and were asked to rate their ice creams on a five-point scale, with 1 being least satisfied and 5 most satisfied. The survey results are summarized in the following table. Construct an interval estimate at 95% confidence interval for difference of means of two ice cream companies b. Write the number of the correct option.

1. The 95% CI is (0.6685 to 1.3385)

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Answer in Statistics and Probability for Kanwal #231427
Just from $13/Page 2. The 95% CI is (0.6685 to 1.3115) 3. The 95% CI is (0.6415 to 1.3385) 4. The 95% CI is (0.6685 to 2.3385) 5. The 95% CI is (1.2146 to 1.3115) Company 1 N1=8 Mean value of sample 1=3.21 standard deviation of sample 1=0.31 Company 2 N2=5 Mean value of sample 2=2.22 standard deviation of sample 2=0.21 Solution: Given: n= 8 “\bar x_1 = 3.21” s1 = 0.31 n2 = 5 “\bar x_2 = 2.22” s2 = 0.21 Assuming both variances are equal: Since samples are less than 30 in this problem we are dealing with t-distirbution with n+ n– 2 = 8 + 5 – 2 = 11 degrees of freedom. The table t-value for a 95% confidence interval with 25 df is t0.025, 11 = 2.201 The formula for a 95% confidence interval for the difference of two population means: “(\bar x_1-\bar x_2)\pm t_{0.025, 11}s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}” where “s_p=\sqrt{\frac{s_1^2(n_1-1)+s_2^2(n_2-1)}{n_1+n_2-2}}” “s_p=\sqrt{\frac{0.31^2\cdot7+0.21^2\cdot4}{8+5-2}}=0.28” Confidence interval: “(3.21-2.22)\pm2.201\cdot0.28\sqrt{\frac{1}{8}+\frac{1}{5}}=0.99\pm0.35” We are 95% confident that the difference in the two population means is between 0.64 and 1.34. Zero is not in this interval so there is a significant difference of means of two ice cream companies. Constructing a confidence interval for the difference of means when both variances are not equal: “(\bar x_1-\bar x_2)\pm t\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}” where df is the smaller of n1–1 and n2–1 df = min(8-1, 5-1)=4 Therefore the table t-value for a 95% confidence interval with 4 df is t0.025, 4 = 2.776 “(3.21-2.22)\pm 2.776\sqrt{\frac{0.31^2}{8}+\frac{0.21^2}{5}}=0.99\pm 0.4” We are 95% confident that the difference in the two population means is between 0.59 and 1.39. Zero is not in this interval so there is a significant difference of means of two ice cream companies. # What Will You Get? We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines. #### Premium Quality Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments. #### Experienced Writers Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals. #### On-Time Delivery Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time. #### 24/7 Customer Support Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern. #### Complete Confidentiality Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret. #### Authentic Sources We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources. #### Moneyback Guarantee Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing. #### Order Tracking You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step. #### Areas of Expertise Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types. # Trusted Partner of 9650+ Students for Writing From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade. ##### Preferred Writer Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen. ##### Grammar Check Report Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document. ##### One Page Summary You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary. ##### Plagiarism Report You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work. ## Free Features$66FREE

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