STATISTICS

# If the claim is the null hypothesis finish the

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If the claim is the null hypothesis, finish the conclusion with “to reject the claim” If the claim is the alternative hypothesis, finish the conclusion with “to support the claim”

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8. The assumptions are as follows: To test a hypothesis test about a population mean, the sample needs to be collected randomly and be either nearly normal or at least 30. To test a hypothesis test about a population percentage (proportion), the sample needs to be collected randomly and n (p) and n (1-p) must both be at least 10. 9. 0 : 180 (claim) : 180 A H H Simulating a population mean of 180 pounds gave the following printout from StatKey. Answers may vary since it is a randomized simulation. The sample mean in the health data was 172.55 pounds. Simulating 2000 times, that sample mean of 172.55 or more extreme occurred a total of 138 times (two tails). This indicates that the chances of the sample data or more extreme data happening from a population of 180 was 0.069 (6.9%). This is an estimated P-value. Since we are using a significance level of 6.9%, we will fail to reject the null hypothesis. There is evidence, but it is not quite significant enough to reject the claim that the average weight of men is 180 pounds. The sample data was unlikely to happen from the population value of 180, but it was not quite unlikely enough. The sample mean 172.55 was different than the population value of 180, but it was not quite significant enough. Conclusion: There is not significant enough evidence to reject the claim that the mean average weight of men is 180 pounds. 10. 0 : 25 : 25 (claim) A H H Right Tailed Test. Test Stat T = 2.204 The sample mean of \$26.82 was 2.204 standard errors above the population value of \$25. There is a significant difference between the sample value and the population value. The sample value was significantly higher than the population value. P-Value = 0.0181 If the average salary of nurses is \$25, then there was only a 1.81% chance of getting the sample data or more extreme. If the average salary really is \$25, then it was very unlikely that the sample data happened by random chance (1.8%). Reject the null hypothesis. There is significant evidence to support the claim that the average salary of nurses is greater than \$25.
11. 0 : p 0.1 : p 0.1 (claim) A H H Right Tailed Test. Answers may vary in simulation. In 5000 simulations we only got a sample percent of 13% or higher only 1 time. Estimated P-value = 0.0004 Reject Ho. The sample value of 13% is significantly higher than the population value of 10%. It is very unlikely (0.0004) that the sample value happened by random chance. There is significant sample evidence to support the claim that the more than 10% of women have at least one tattoo. 12. 0 : p 0.25 (claim) : p 0.25 A H H Two tailed test. The sample percent was 0.259 and the Z test Stat = 0.197 . So the sample percent was only 0.197 standard errors above the population value. This is very close. They are not significantly different. The Pvalue = 0.8435 So if the population value is 25%, there was an 84.4% chance of getting the sample data or more extreme.

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• Fall '17
• Statistics, Statistical hypothesis testing, significant sample evidence

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