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A sample of 40 observations is selected from one approximately normal population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second source. The sample mean is 99 and the standard deviation is 6. Conduct a hypothesis test using the .04 level of significance to determine if there is a difference between the population means.

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    I'll give you a few hints. Try a two-sample z-test on this data since the sample sizes are fairly large. In symbolic form, the null hypothesis would state the population means are equal and the alternate hypothesis would state the populations are not equal. If the null is rejected in favor of the alternate hypothesis at .04 level of significance (you can determine the cutoff or critical z to reject the null from a z-table), you can then conclude a difference in the population.

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    Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking-even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were place (individually) in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights on and off as they wished. After one month in the room, each individual tended to develop a steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.

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