Hypothesis Test for a Population Mean (o is Unknown) You wish to test the following claim (Ha) at a significance level of a = 0.01. Ho:µ = 73.1 Ha:µ > 73.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 223 with mean M = 74 and a standard deviation of SD = 5.2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null accept the null fail to reject the null

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Test the claim that the mean GPA of night students is smaller than 2.2 at the .10 significance level. Based on a sample of 45 people, the sample mean GPA was 2.16 with a standard deviation of 0.06The test statistic is:  (to 2 decimals)The critical value is:  (to 2 decimals)

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UNKNOWN STANDARD DEVIATION

A new material will replace the old material only if there is significant evidence that the mean strength of the new material is more than 2 units higher than the mean strength of the old material.        Sample from new material:     mean  is  98.064   ,     SD  is   5.6     and sample size is 13 Sample from old material:       mean  is  95.282   ,     SD  is   5.8      and sample size is 78 We do not know population standard deviations. Consider the test           ?0:????−????=2H0:μnew−μold=2   vs.  ?0:????−????>2H0:μnew−μold>2  What is the p-value?       (Hint:  best to use software, or else the Desmos Calculator for the 2 sample T and Z test)  Give as a decimal between 0 and 1 accurate to at least 4 decimal places.

The mean number of eggs per person eaten in the United States is 252 and the standard deviation is 68. Do college students eat more than the average? The 45 college students surveyed averaged 281 eggs per person. What can be concluded at the 0.05 level of significance? H0: = 252 Ha: _____________ 252 Test statistic: __________    p-Value =__________                    Reject/Fail to reject H0?______________         Conclusion: There is____________   evidence to make the conclusion that the population mean number of eggs consumed college students per year is more than 252 eggs per student per year. p-Value Interpretation: If the mean number of eggs consumed per year for college students is equal to_________  and if another study was done with a new randomly selected group of 45 college students, then there is a ____________ percent chance that the average number of eggs consumed per year for this new sample would be greater than_____________        . Level of significance…

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