Suppose 55% of people in Georgia support a special transportation tax. Alejandro is not confident that this claim is correct. To investigate the claim, he surveys 150 people in his community and discovers that 54 people support a special transportation tax. Calculate Alejandro's sample proportion, ?̂. Give your answer precise to two decimal places. Calculate the standard error of the sample proportion, SE. Give your answer precise to three decimal places. Calculate the standard error of the sample proportion estimate, SEest. Give your answer precise to three decimal places.
The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the ages of 6 and 16. The test is standardized so that the mean score for all children is 100 and the standard deviation is 15.
Suppose that the administrators of a very large and competitive school district wish to estimate the mean WISC score for all students enrolled in their programs for gifted and talented children. They obtained a random sample of 40 students currently enrolled in at least one program for gifted and talented children. The test scores for this sample are as follows:
| 106 | 142 | 110 | 123 | 135 | 114 | 119 | 118 | 121 | 95 | 154 | 119 | 109 | 131 | 130 | 98 | 117 | 105 | 143 | 94 |
| 110 | 167 | 117 | 98 | 125 | 133 | 122 | 98 | 116 | 126 | 127 | 114 | 124 | 134 | 133 | 102 | 125 | 109 | 124 | 109 |
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Use this data to calculate the mean WISC score, ?⎯⎯⎯, for these 40 students. Next, compute the standard deviation, SD, of the sampling distribution of the sample mean, assuming that the standard deviation of WISC scores for students in the district is the same as for the population as a whole. Finally, determine both the lower and upper limits of a 95% ?-confidence interval for ?, the mean score for all students in the school district who are enrolled in gifted and talented programs.
Give ?⎯⎯⎯ and the limits of the confidence interval precise to one decimal place, but give the standard deviation to at least three decimal places in order avoid rounding errors when computing the limits.
3.
Researchers are planning a study to estimate the impact on crop yield when no-till is used in combination with residue retention and crop rotation. Based on data from a meta-analysis of 610 small farms, the researchers estimate there is a 2.5% decline in crop yield when no-till is used with residue retention and crop rotation. Suppose the researchers want to produce a 95% confidence interval with a margin of error of no more than 1.0%. Determine the minimum sample size required for this study.
The sample size needed to create a confidence
Researchers are planning a study to estimate the impact on crop yield when no-till is used in combination with residue retention and crop rotation. Based on data from a meta-analysis of 610 small farms, the researchers estimate there is a 2.5% decline in crop yield when no-till is used with residue retention and crop rotation. Suppose the researchers want to produce a 95% confidence interval with a margin of error of no more than 1.0%. Determine the minimum sample size required for this study.
The sample size needed to create a confidence interval estimate depends on the margin of error, the initial estimated proportion, and the confidence level. Be sure to use proportions rather than percentages. Round your final answer up to the nearest whole number.
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