Question

An experienced census official feels that she can accurately estimate the number of inhabitants of a city block by simply noting the size of the block and the types of buildings (single family homes, apartments, businesses, etc.) that are found on the block. This procedure, if accurate, would be much quicker and cheaper than visiting each residence and taking a survey of its inhabitants. The data below are estimates of block populations provided by the official for 10 blocks in a large city, and the actual numbers of inhabitants for the same 10 blocks. Inhabitants of City Blocks Estimate 193 86 81 87 223 226 151 126 120 76 Actual 163 140 150 179 204 128 73 89 136 145 Step 1 of 2: Find the value of the test statistic for testing whether there is a linear relationship between the actual number of inhabitants and the estimated number. Round your answer to two decimal places, if necessary.

Answer 1

Answer:

035

Step-by-step explanation:

193

86

81

87

223

226

151

126

120

76

Y:

163

140

150

179

204

128

73

89

136

145

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35