6) A special diet is intended to reduce systolic blood pressure. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 15 patients with high blood pressure was evaluated; the data are shown below along with a stem plot of the data. Is this sufficient evidence that the diet is effective in meeting the target? Answer in the blanks to show the work associated with exploring this claim. Data: 130 120 140 142 153 170 145 150 155 148 160 140 138 144 125 Stem plot of Data (key, 13|0 means 130): 12|0 5 13|0 8 14|0 0 2 4 5 8 15|0 3 5 16|0 1 7|0 a) Assume that the fifteen measurements can be treated as an SRS from this population. Since we are not told that we are sampling from a normal population and n is not large, then it is important that the data is reasonably symmetric to be able to continue. Judging from the given stem plot, is the data reasonably symmetric (yes or no)? Conduct a significance test to explore the above suspicion. To do so, use the hypotheses: H0: μ=150 HA: μ<150 b) Report the test statistic to two decimal places. c) Report the p-value to four decimal places d) Give the test decision: (reject or do not reject) e) Evidence _______________(favors or does not favor) that with use of the special diet, patients blood pressure is below 150 on average.
= 150, n = 15, = 144, SD(S) = 13.07, = 0.05
Ho: = 150
Ha: < 150
Degree of freedom = n-1 = 15-1 = 14
P-value = 0.0486 ...................Using t table
P-value < α, i.e. 0.0486 < 0.05, That is Reject Ho at 5% level of significance.
Evidence favors that with use of the special diet, patients blood pressure is below 150 on average.
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