The assessment of diet is an important exposure for many disease outcomes. However, there is often much imprecision in dietary recall. In one study, 70- to 79-year-old women were asked about the preschool diet of their children (ages 2-4)using a food frequency questionnaire (FFQ). A unique aspect of the study is that simultaneous diet record data exist on the same children recorded in real time by their mothers when they were ages 2-4 and their mothers were 20 to 40 yearsold. The data in the table below were available on average servings of margarine per week.Margarine IntakeAssessed by Two DifferentRecording Methods(Servings per Week,[n = 12])ID340H₁:399466502541554558605611618653707FFQ77000777210217DR00.50002.43.10.53.62.34.28.6The Pearson correlation between intake from the two recording methods was 0.4500. Assume that FFQ and DR margarine intake are normally distributed.You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question.(a) Test the hypothesis that the true Pearson correlation (p) is significantly different from zero [provide a p-value (two-tailed)]. (Use α = 0.05.)State the null and alternative hypotheses. (Enter != for as needed.)Ho:Calculate the test statistic. (Round your answer to two decimal places.)Use technology to find the p-value. (Round your answer to four decimal places.)p-value = State your conclusion.O Reject Ho. There is insufficient evidence to conclude that the true Pearson correlation is different from zero.O Reject Ho. There is sufficient evidence to conclude that the true Pearson correlation is different from zero.Fail to reject Ho. There is sufficient evidence to conclude that the true Pearson correlation is different from zero.O Fail to reject Ho. There is insufficient evidence to conclude that the true Pearson correlation is different from zero.(b) Provide a 95% confidence interval for p. (Enter your answer using interval notation. Round your numerical values to three decimal places.)The distribution of dietary intake for individual food items is often not very normally distributed.An alternative measure of correlation between the FFQ and DR that does not depend on the assumption of normality is the Spearman rank correlation (r). For the margarine data, r = 0.6968.(c) Test the hypothesis that the Spearman rank correlation is significantly different from 0 [provide a p-value (two-tailed)]. (Use α = 0.05.)State the null and alternative hypotheses. (Enter != for as needed.)Ho:H₁:Calculate the test statistic. (Round your answer to two decimal places.)Use technology to find the p-value. (Round your answer to four decimal places.)p-value =State your conclusion.Reject Ho. There is sufficient evidence to conclude that the true Spearman rank correlation is different from zero.Fail to reject Ho. There is insufficient evidence to conclude that the true Spearman rank correlation is different from zero.O Reject Ho. There is insufficient evidence to conclude that the true Spearman rank correlation is different from zero.Fail to reject Ho. There is sufficient evidence to conclude that the true Spearman rank correlation is different from zero.(d) Provide a 95% confidence interval for the true Spearman rank correlation (p). (Enter your answer using interval notation. Round your numerical values to three decimal places.)

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