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In a survey of 100 randomly selected people in City A, 81 support increased government spending on education. In a survey of 100 randomly selected people in City B, 87 support such spending. Test the alternative hypothesis that the population proportion of people in City A who support such spending is less than the population proportion of people in City B who do. The test statistic is [tex]$z = -1.16$[/tex]. What is the corresponding [tex][tex]$p$[/tex]-value[/tex]? Compute your answer using a value from the table below.

\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline [tex]$z$[/tex] & 0.00 & 0.01 & 0.02 & 0.03 & 0.04 & 0.05 & 0.06 & 0.07 & 0.08 & 0.09 \\
\hline -2.0 & 0.023 & 0.022 & 0.022 & 0.021 & 0.021 & 0.020 & 0.020 & 0.019 & 0.019 & 0.018 \\
\hline -1.9 & 0.029 & 0.028 & 0.027 & 0.027 & 0.026 & 0.026 & 0.025 & 0.024 & 0.024 & 0.023 \\
\hline -1.8 & 0.036 & 0.035 & 0.034 & 0.034 & 0.033 & 0.032 & 0.031 & 0.031 & 0.030 & 0.029 \\
\hline -1.7 & 0.045 & 0.044 & 0.043 & 0.042 & 0.041 & 0.040 & 0.039 & 0.038 & 0.038 & 0.037 \\
\hline -1.6 & 0.055 & 0.054 & 0.053 & 0.052 & 0.051 & 0.049 & 0.048 & 0.047 & 0.046 & 0.046 \\
\hline -1.5 & 0.067 & 0.066 & 0.064 & 0.063 & 0.062 & 0.061 & 0.059 & 0.058 & 0.057 & 0.056 \\
\hline -1.4 & 0.081 & 0.079 & 0.078 & 0.076 & 0.075 & 0.074 & 0.072 & 0.071 & 0.069 & 0.068 \\
\hline -1.3 & 0.097 & 0.095 & 0.093 & 0.092 & 0.090 & 0.089 & 0.087 & 0.085 & 0.084 & 0.082 \\
\hline -1.2 & 0.115 & 0.113 & 0.111 & 0.109 & 0.107 & 0.106 & 0.104 & 0.102 & 0.100 & 0.099 \\
\hline -1.1 & 0.136 & 0.133 & 0.131 & 0.129 & 0.127 & 0.125 & 0.123 & 0.121 & 0.119 & 0.117 \\
\hline -1.0 & 0.159 & 0.156 & 0.154 & 0.152 & 0.149 & 0.147 & 0.145 & 0.142 & 0.140 & 0.138 \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
To determine the corresponding [tex]\( p \)[/tex]-value for the given [tex]\( z \)[/tex]-score of [tex]\(-1.16\)[/tex], we will use the provided z-table. Here's a step-by-step guide:

1. Identify the [tex]\( z \)[/tex]-score of interest:
The [tex]\( z \)[/tex]-score provided is [tex]\(-1.16\)[/tex].

2. Locate the row corresponding to the integer and first decimal place of the [tex]\( z \)[/tex]-score:
For [tex]\(-1.16\)[/tex], the integer and first decimal place are [tex]\(-1.1\)[/tex]. Locate the row for [tex]\(-1.1\)[/tex].

3. Locate the column corresponding to the hundredth decimal place of the [tex]\( z \)[/tex]-score:
For [tex]\(-1.16\)[/tex], the second decimal place is [tex]\(0.06\)[/tex]. Locate the column for [tex]\(0.06\)[/tex].

4. Find the intersection of the row and column:
Find where the row for [tex]\(-1.1\)[/tex] and the column for [tex]\(0.06\)[/tex] intersect in the table.

Based on the provided table, the intersection of the row [tex]\(-1.1\)[/tex] and column [tex]\(0.06\)[/tex] gives the following value:

[tex]\[ p = 0.123 \][/tex]

Thus, the corresponding [tex]\( p \)[/tex]-value for the [tex]\( z \)[/tex]-score of [tex]\(-1.16\)[/tex] is 0.123.
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