An SRS of 100 postal employees found that the average time these employees had worked at the postal service was years with standard deviation years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of that was true years ago? To determine this, we test the hypotheses versus using a one-sample test. What conclusion should we draw at the significance level?
(a) There is convincing evidence that the mean time working with the postal service has changed.
(b) There is not convincing evidence that the mean time working with the postal service has changed.
(c) There is convincing evidence that the mean time working with the postal service is still years.
(d) There is convincing evidence that the mean time working with the postal service is now years.
(e) We cannot draw a conclusion at the significance level. The sample size is too small.
The answer is (a). There is convincing evidence that the mean time working with the postal service has changed.
Determine the value of the test statistic:
The value is the chance of getting the test statistic's result, or a number that is more severe. The value is the number (or interval) in Table IV's column title that corresponds to the row's value.localid="1650366176477"
The null hypothesis is rejected if the value is less than the significance level.
There is convincing evidence that the meantime working with the postal service has changed.
Your company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements. Based on the sample results, the device determines whether there is significant evidence that the individual’s actual mean systolic pressure is greater than 130. If so, it recommends that the person seek medical attention.
(a) State appropriate null and alternative hypotheses in this setting. Be sure to define your parameter.
(b) Describe a Type I and a Type II error, and explain the consequences of each.
(c) The blood pressure device can be adjusted to decrease one error probability at the cost of an increase in the other error probability. Which error probability would you choose to make smaller, and why?
Are TV commercials louder than their surrounding programs? To find out, researchers collected data on randomly selected commercials in a given week. With the television’s volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is
(a) a one-proportion z test.
(b) a one-proportion z interval.
(c) a paired t test.
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