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For the sample collected ten years earlier,

The size of the sample is $n_1=797$.

The proportion of commercials that use religious symbolism is

$\begin{array}{rcl}{\hat{p}}_1& =& \frac{x_1}{n_1}\\ & =& \frac{16}{797}\\ & =& 0.0201\end{array}$

Also, for the sample collected more recently

The size of the sample is $n_2=1499$.

The proportion of commercials that use religious symbolism is

$$\begin{gathered} {\hat{p}}_2=\frac{x_2}{n_2} \\ =\frac{51}{1499} \\ =0.0340 \end{gathered}$$

Hypothesis testing is the process of testing the statements made by the researcher or any other concerned person using the probability sampling method's sample data.

We have to test whether the percentage of TV commercials that use religious symbolism has changed over time or not.

Let

$p_1:$The population proportion of commercials used religious symbolism ten years earlier.

$p_2:$The population proportion of commercials recently used religious symbolism.

The null and alternative hypotheses are

$H_0:p_1=p_2$

The percentage of TV commercials that use religious symbolism has not changed.

Against

$H_a:p_1鈮�p_2$

The percentage of TV commercials that use religious symbolism has changed over time.

The test statistic for testing these hypotheses is

$$\begin{gathered} Z=\frac{{\hat{p}}_1-{\hat{p}}_2}{\sqrt{\frac{{\hat{p}}_1\left(1-{\hat{p}}_1\right)}{n_1}+\frac{{\hat{p}}_2\left(1-{\hat{p}}_2\right)}{n_2}}} \\ =\frac{0.0201-0.0340}{\sqrt{\frac{0.0201\left(1-0.0201\right)}{797}+\frac{0.0340\left(1-0.0340\right)}{1499}}} \\ =\frac{-0.0139}{\sqrt{0.000024713+0.000021911}} \\ =\frac{-0.0139}{0.00683} \\ =-2.04 \end{gathered}$$

The p-value for the obtained test statistic is

$$\begin{gathered} p-value=2脳P\left(Z>\left|z\right|\right) \\ =2脳P\left(Z>2.04\right) \\ =2脳\left(1-P\left(Z猢�2.04\right)\right) \\ =2脳\left(1-0.9793\right) \\ =2脳0.0207 \\ =0.0414 \end{gathered}$$

We can see that

$p-value<0.05$

Hence, we reject the null hypothesis $H_0$.

At a 5% significance level, we have sufficient evidence to conclude that the percentage of TV commercials that use religious symbolism has changed over time.

The magnitude of the difference is given as

$\begin{array}{rcl}d& =& \left|{\hat{p}}_1-{\hat{p}}_2\right|\\ & =& \left|0.0201-0.0340\right|\\ & =& 0.0139\end{array}$

The measure of reliability cannot be computed here, as the true difference between the population proportions is unknown.