# Answer in Statistics and Probability for Goldie #254478

TWO DEPENDENT SAMPLE MEANS.

Use the traditional method in testing hypothesis.

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Answer in Statistics and Probability for Goldie #254478
Just from $13/Page Developmental psychologists at a prominent California university conducted a longitudinal study investigating the effect of high levels of curiosity in early childhood on intelligence. The local population of 3-year-olds was screened via a test battery assessing curiosity. Twelve of the 3-year-olds scoring in the upper 90% of this variable were given an IQ test at age 3 and again at age 11. The following IQ scores were obtained. Student Number: 1 2 3 4 5 6 7 8 9 10 11 12 IQ (Age of 3) : 100 105 125 140 108 122 117 112 135 128 104 98 IQ (Age of 11) : 114 116 139 151 106 119 131 136 148 139 122 113 Using ∝= 0.01, two-tailed test, analyse the data and then interpret the result. In this question, we have a case where our sample is dependent and we should first consider using matched/paired t-test for our analysis. To perform this test, we begin by finding the difference between pairs of observation for each child. We shall use the notation “d,” to represent the differences and use it to make a decision. The hypotheses to be tested are, “H_0:\mu_d=0” “Against” “H_1:\mu_d\not=0”, where “d” is the difference between each pair of observations. To test these hypotheses, we first determine the mean of the differences“(\bar{d})” given by, “\bar{d}=(\sum(d))/n”, where “n=12.” Now, “\sum(d)=-140” Therefore, “\bar{d}=-140/12=-11.66666667” Variance of the differences is given by, “V(d)=\sum(d-\bar{d})^2/(n-1)” “V(d)=624.666666667/11=56.78788(5\space d\space p)”. The standard deviation “SD(d)” is given by, “SD(d)=\sqrt{V(d)}=\sqrt{56.78788}=7.535773271”. The test statistic is given by, “t^*=\bar{d}/(SD(d)/\sqrt n)” “t^*=-11.66666667/(7.535773271/\sqrt {12})” “t^*=-11.66666667/2.175390363=-5.363022133.” “t^*” is compared with the student’s t distribution with “(n-1)=12-1=11” degrees of freedom at “\alpha=0.01”. The table value “t_{\alpha/2,11}=t_{0.01/2,11}=t_{0.005,11}=3.106” and reject the null hypothesis if “|t^*|\gt t_{0.005,11}.” Since “|t|=5.363\gt t_{0.005,11}=3.106,” we reject the null hypothesis and conclude that sufficient evidence exists to show that high levels of curiosity in childhood affect IQ. They seem to increase the IQ. # 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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