A study believes that 70% of adults in the Philippines own a cellphone.
A cellphone manufacturer believes that the actual number is much
less than 70%. 100 Filipino adults were surveyed, of which 74 have
cellphones. Using a 5% level of significance, is the cellphone
manufacturer’s claim valid or not?
Claim: the actual number is much less than 70%.
The following null and alternative hypotheses for the population proportion needs to be tested:
This corresponds to a left-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 left-tailed test is
The rejection region for this left-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 less than 0.70, at the significance level.
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