a)

A one-sample z test is carried out to check a population mean is equal to a given value or not. The observed test statistic of the test was -1.297. What is the R command to obtain the P-value in this case? O 2 * qt(-1.297, 0, 1) O 2 * qnorm(-1.297, 0, 1) O 2 * qnorm(1.297, 0, 1) O 2 * q1(1.297, 0, 1) O 2 * pnorm(-1.297, 0, 1) O 2 * phorm(1.297, 0, 1)An ambulance service claims that it takes, on the average, 7 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has decided to carry out a one-sample t test. From a sample of 36 emergency calls they have obtained a sample mean of 6.4 minutes and the standard deiviation as 4.6 minutes. Calculate the observed test statistic to check the claim of the ambulance service? Provide your answer to 3 decimal placesWe took a random sample of 150 observations from a normal distribution with known standard derivation o = 19. The sample mean of this sample was 99.22. WhiCh of the following is the corresponding 95% condence interval for the mean? Consider critical value as 1.96. C: [95.13. 1:112:51 Q {9167, most) (:3 {95.57, 1111.7?) 0 (9153.111035] Suppose the 95% confidence interval for the population mean head circumference of two-month- old babies is (36.01, 42.44) in centimetres. What is the correct interpretation of this confidence interval? O We are 95% confident that the true mean head circumference of two-month-old babies lies between 36.01 and 42.44 centimetres. O We are 95% confident that the sample mean head circumference of two-month-old babies lies between 36.01 and 42.44 centimetres. O The probability that the true mean head circumference of two-month-old babies lies between 38.01 and 44.44 centimetres is 0.95. O We are 90% confident that the true mean head circumference of two-month-old babies lies between 36.01 and 42.44 centimetres