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Out of 420095 cell phone users, 135 develop cancer of the brain or nervous system. It is claimed that the rate at which cell phone users develop cancer is not equal to 0.0340%.

The null hypothesis is written as follows.

The proportion of cell phone users who develop cancer is equal to 0.0340%.

\({H_0}:p = 0.000340\).

The alternative hypothesis is written as follows.

The proportion of cell phone users who develop cancer is not equal to 0.0340%.

\[{H_1}:p \ne 0.000340\].

The test is two-tailed.

The sample size is equal to n=420095.

The sample proportion of cell phone users who develop cancer is computed below.

\[\begin{array}{c}\hat p = \frac{{{\rm{Number}}\;{\rm{of}}\;{\rm{users}}\;{\rm{who}}\;{\rm{developed}}\;{\rm{cancer}}}}{{{\rm{Sample}}\;{\rm{Size}}}}\\ = \frac{{135}}{{420095}}\\ = 0.000321\end{array}\]

The population proportion ofcell phone users who develop cancer is equal to 0.000340.

The value of the test statistic is computed below.

\(\begin{array}{c}z = \frac{{\hat p - p}}{{\sqrt {\frac{{pq}}{n}} }}\\ = \frac{{0.000321 - 0.000340}}{{\sqrt {\frac{{0.000340\left( {1 - 0.000340} \right)}}{{420095}}} }}\\ = - 0.667\end{array}\).

Thus, z=-0.667.

Referring to the standard normal table, the critical value of z at\(\alpha = 0.005\)for a two-tailed test is equal to 2.807.

Referring to the standard normal table, the p-value for the test statistic value of -0.667 is equal to 0.5047.

Asthe p-value is greater than 0.005, the null hypothesis is failed to reject.

There is not enough evidence to support the claim that the proportion of cell phone users who develop cancer of the brain or nervous system is not equal to 0.0340%.

Asthe results suggest that the proportion of cell phone users, as well as non-cell phone users who develop cancer, is approximately the same, cell phone users should not be concerned.