A local political leader claims that 95% of the families in his area of responsibility
were given “ayuda” during a one-month lockdown. Of a random sample of 200 families, 187 said they received relief or “ayuda”. Is this enough to affirm the
leader’s claim? Use 𝑎 = 0.05.
The following null and alternative hypotheses for the population proportion needs to be tested:
This corresponds to a two-tailed test, for which a z-test for one population proportion will be used.
Evidence:
Based on the information provided, the significance level is and the critical value for a two-tailed test is
The rejection region for this two-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population proportion is different than 0.95, at the significance level.
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