You wish to test the following claim (Ha) at a significance level of a = 0.01. H.: µ = 68.6 Ha: u + 68.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 503 with mean M = 64.9 and a standard deviation of SD = 19.6. 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... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 68.6. O There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 68.6. O The sample data support the claim that the population mean is not equal to 68.6. O There is not sufficient sample evidence to support the claim that the population mean is not equal to 68.6.

You wish to test the following claim (Ha) at a significance level of a = 0.002. Ha:µ < 78.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 19 with mean = 70.4 and a standard deviation of s = 19.8. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is. Oless than (or equal to) a Ogreater than a This p-value leads to a decision to. Oreject the null Oaccept the null Ofail to reject the nul As such, the final conclusion is that. OThere is sufficient evidence to warrant rejection of the claim tha: the population mean is less than 78.6. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 78.6. OThe sample data support the claim that the population mean is less than 78.6. OThere is not sufficient sample evidence to support the claim that the population mean is less than 78.6.

This assignment is worth 1 points. The extra point will be added to your overall course grade. For example: if you receive an 88% in the course you can receive up to 1 point giving you a new score of 89%. The following rubric will be used.  0.25 point for drawing the normal distribution curve with the mean value labeled on the curve and the appropriate area shaded. 0.25 point for determining the value of the standard deviation of the sample mean.  0.5 point for finding the correct probability.   All work must be shown in order to receive any credit.  Please upload your completed assignment here.    The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.

You wish to test the following claim (Ha) at a significance level of a = 0.001. H.:µ = 59.3 Ha:µ + 59.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 666 with mean M = 57.9 and a standard deviation of SD = 15.4. 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 Ogreater than a This test statistic leads to a decision to... reject the null |accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 59.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 59.3. The sample data support the claim that the population mean is not equal…