# Answer in Statistics and Probability for Hunter #272360

The data below gives the end year profit in million shillings of twelve randomly selected pharmaceutical firms in Nairobi county;71.2,52.7,95.7,63.5,91.8,102.7,87.6,77.9,81.8,90.1,123.7,79.9.It is known that the average end of year profit of the twelve firms is 89.91m. An average value less than 89.91m is considered unacceptable.

a.)Test the null hypothesis at 5% level of significance. What is the value of your standard deviation, tabulated and calculated test static and decision?

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Answer in Statistics and Probability for Hunter #272360
Just from $13/Page b.) Construct a 95% confidence interval for the sample mean “mean=\bar{x}=\dfrac{1}{12}\sum_ix_i=\dfrac{1017.7}{12}” “\approx84.8083” “s^2=\dfrac{1}{12-1}\sum _i(x_i-\bar{x})^2\approx345.151742” “s=\sqrt{345.151742}\approx18.57826” a) The following null and alternative hypotheses need to be tested: “H_0:\mu\geq89.91” “H_1;\mu<89.91” This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used. Based on the information provided, the significance level is “\alpha = 0.05,” “df=12-1=11” degrees of freedom, and the critical value for a left-tailed test is “t_c = -1.795885.” The rejection region for this left-tailed test is “R = \{t: t < -1.795885\}.” The t-statistic is computed as follows: “t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{84.8083-89.91}{18.57826/\sqrt{12}}” “=-0.951263” Since it is observed that “t = -0.951263 \ge -1.795885=t_c ,” it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value for left-tailed, “\alpha=0.05, df=11” degrees of freedom, “t = -0.951263” is “p=0.180952,” and since “p= 0.180952>0.05=\alpha,” it is concluded that the null hypothesis is not rejected. Therefore, there is not enough evidence to claim that the population mean “\mu” is less than “89.91,” at the “\alpha = 0.05” significance level. b) The critical value for “\alpha = 0.05” and “df = n-1 = 11” degrees of freedom is “t_c = z_{1-\alpha/2; n-1} = 2.200985.” The corresponding confidence interval is computed as shown below: “CI=(\bar{x}-t_c\times\dfrac{s}{\sqrt{n}}, \bar{x}+t_c\times\dfrac{s}{\sqrt{n}})” “=(84.8083- 2.200985\times\dfrac{18.57826}{\sqrt{12}},” “84.8083+2.200985\times\dfrac{18.57826}{\sqrt{12}})” “=(73.004, 96.612)” Therefore, based on the data provided, the 95% confidence interval for the population mean is “73.004 < \mu < 96.612,” which indicates that we are 95 % confident that the true population mean “\mu” is contained by the interval “(73.004, 96.612).” # 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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