Problem 6 In the Spacelab Life Sciences payload, 14 random male rats were sent to space Upon their return, the red blood cell mass (in millimeters) of rats was determined A control group of 14 random male rats was held under same conditions (except for space flight) as the space rats, and their red blood cell mass was also determined when the space rats returned The project, led by Dr Paul X Callahan, resulted in the data listed below Flight 6 8, 8 64,7 43, 7 21, 6 87, 7 89, 9 79, 6 85, 7 00, 8 80, 9 30, 8 03, 6 39, 7 54 Control 8 65, 6 99, 8 40, 9 66, 7 62, 7 44, 8 55, 8 70, 7 33, 8 58, 9 88, 9 94, 7 14, 9 14 Use the following R command to input the data Use R to find the sample mean and sample standard deviation for each group Copy and paste you R output Round your answers to three decimal places Show formu a with numbers plugged in to verify that the Standard error for the difference between the sample means is about 0 3853738 Interpret this value What is the value of t multiplier,, to construct a 99 confidence interval Copy and paste your R command and output Show formula with numbers plugged in to verify that 99 confidence interval to estimate the difference between two population mean is ( 1 84, 0 48) Interpret Now use the t test () command in R to construct the 99 codnfidence interval Note to students R uses Welch's degrees of freedom instead of the minimum of n 1 1, n 2 1, hence giving a slightly different 99 CI Problem 7 Use the same information from Problem 6 to conduct a hypothesis test to find out if the evidence suggests that the flight animals have a lower red blood cell mass than the control animals at the alpha 0 1 level of significance Assume that the data could come from populations that are normal (Do not use t test() Assumptions Hypotheses Test statistic what is the distribution of test statistic Based on the sample information provided in problem 6, what is the value of the test statistic P value Conclusion and interpretation in context Refer to the conclusion from this problem Based on the conclusion (reject the null or fail to reject the null), what type of error (either Type 1 or Type 2) could you have made Problem 8 Use the R command t test() to repeat Problem 7 (conduct a hypothesis test to find out if the evidence suggests that the flight animals have a lower red blood cell mass than the control animals at the alpha 0 1 level of significance) Copy and paste your R command and output Note to students R uses Welch's degrees of freedom instead of the minimum of n 1 1, n 2 1, hence giving a slightly different p value from Problem 7

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Problem 6. In the Spacelab Life Sciences payload, 14 random male rats were sent to space. Upon their return, the red blood cell mass (in

Problem 6.In the Spacelab Life Sciences payload, 14 random male rats were sent to space. Upon their return, the red blood cell mass (in millimeters) of rats was determined. A control group of 14 random male rats was held under same conditions (except for space flight) as the space rats, and their red blood cell mass was also determined when the space rats returned. The project, led by Dr. Paul X. Callahan, resulted in the data listed below.

Flight: 6.8, 8.64,7.43, 7.21, 6.87, 7.89, 9.79, 6.85, 7.00, 8.80, 9.30, 8.03, 6.39, 7.54

Control: 8.65, 6.99, 8.40, 9.66, 7.62, 7.44, 8.55, 8.70, 7.33, 8.58, 9.88, 9.94, 7.14, 9.14

Use the following R command to input the data.

Use R to find the sample mean and sample standard deviation for each group. Copy and paste you R output.Round your answers to three decimal places
Show formu;a with numbers plugged in to verify that the Standard error for the difference between the sample means is about 0.3853738. Interpret this value.
What is the value of t-multiplier,, to construct a 99% confidence interval? Copy and paste your R command and output.
Show formula with numbers plugged in to verify that 99% confidence interval to estimate the difference between two population mean is (-1.84, 0.48). Interpret.
Now use the t.test () command in R to construct the 99% codnfidence interval. Note to students: R uses "Welch's degrees of freedom" instead of the minimum of n₁- 1, n₂- 1, hence giving a slightly different 99% CI

Problem 7.Use the same information from Problem 6 to conduct a hypothesis test to find out if the evidence suggests that the flight animals have a lower red blood cell mass than the control animals at the alpha = 0.1 level of significance. Assume that the data could come from populations that are normal (Do not use t.test()

Assumptions:
Hypotheses
Test statistic: what is the distribution of test statistic? Based on the sample information provided in problem 6, what is the value of the test statistic?
P-value
Conclusion and interpretation in context.
Refer to the conclusion from this problem. Based on the conclusion (reject the null or fail to reject the null), what type of error (either Type 1 or Type 2) could you have made?

Problem 8.Use the R command t.test() to repeat Problem 7. (conduct a hypothesis test to find out if the evidence suggests that the flight animals have a lower red blood cell mass than the control animals at the alpha = 0.1 level of significance). Copy and paste your R command and output. Note to students: R uses: "Welch's degrees of freedom" instead of the minimum of n₁-1, n₂- 1, hence giving a slightly different p-value from Problem 7.