DIRECTIONS: In each problem below, give the null and alternative hypothesis and
identify whether it is right-tailed, left-tailed or two-tailed test.
3. A quality control engineer is testing the battery life of a new smartphone. The company
is advertising that the battery lasts 24 hours on full- charge, but the engineer suspects that the
battery life is actually less than that. They take a random sample of 50 of these if their average
battery life is significantly less than 34 hours.
4. In the past, the mean running time for a certain type of radio battery has been 9.6 hours.
The manufacturer has introduced a change in then production method and wants to perform a
hypothesis test to determine whether the mean running time has changed as a result.
5. In a random sample of 400 electronic gadgets, 14 were found to be defective. The
manufacturer wants to claim that more than 5% of all the gadgets are defective. Test this claim at
the 0.01 level of significance.
3. The null hypothesis states that the battery life of a new smartphone will be greater than or equal to 24 hours.
The alternative hypothesis states that the battery life of a new smartphone will be less than 24 hours.
B. This corresponds to a left-tailed (directional, one-tailed) test.
4. The null hypothesis states that the mean running time for a certain type of radio battery will be equal to 9.6 hours.
The alternative hypothesis states that the mean running time for a certain type of radio battery will not be equal to 9.6 hours.
B. This corresponds to a two-tailed test.
5. The following null and alternative hypotheses need to be tested:
This corresponds to a right-tailed test, for which a z-test for one population proportion will be used.
Based on the information provided, the significance level is and the critical value for a right-tailed test is
The rejection region for this right-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 for right-tailed, is and since it is concluded that the null hypothesis is notrejected.
Therefore, there is not enough evidence to claim that the population proportion is more than 5%, at the significance level.
Comments