Question

let X be a random variable that represents the pH of arterial plasma for healthy adults the mean of the X distribution is Mew equals 7.4 a drug for arthritis has been developed however it is thought that this drug may change blood pH a random sample of 36 patients with arthritis took the drug for 3 months blood test showed that the bar x equals 8.4 with sample standard deviation s equals 2.8 use a 5% level of significance to test the claim that the drug has changed either way the mean pH level of the blood hey what is the level of significance State the null and alternative hypothesis what sampling distribution will you use explain the rationale for your choice of sampling distribution what is the value of the sample test statistic run answer to three decimal places estimate the p-value sketch the sampling distribution of show the area corresponding to the P value based on your answers in Parts a & C will you reject or fail to reject the null hypothesis are the data statistically significant at level a interpret your conclusion in the context of the

Answer 1

State the null and alternative hypothesis

H0 : Mean pH level of the sample is equal to 7.4
H1 : Mean pH level of the sample is not equal to 7.4

what sampling distribution will you use explain the rationale for your choice of sampling distribution
We use a student t distribution because the population standard deviation is unknown

what is the value of the sample test statistic run answer to three decimal places
T statistic = 2.143

estimate the p-value
p-value = 0.0392

sketch the sampling distribution of show the area corresponding to the P value

based on your answers in Parts a & C will you reject or fail to reject the null hypothesis are the data statistically significant at level a interpret your conclusion in the context of the
We reject the null hypothesis as the p-value is less than 0.05. Hence we conclude that there is sufficient evidence to claim that the drug has changed either way the mean pH level of the blood