how to do this stat in matlab?

8-54. An article in Cancer Research [“Analyses of Litter-Matched Time-to-Response Data, with Modifications for Recovery of Interlitter Information” (1977, Vol. 37, pp. 3863-3868)] tested the tumorigenesis of a drug. Rats were randomly selected from litters and given the drug. The times of tumor appearance were recorded as follows: 101, 104, 104, 77, 89, 88, 104, 96, 82, 70, 89, 91, 39, 103, 93, 85, 104, 104, 81, 67, 104, 104, 104, 87, 104, 89, 78, 104, 86, 76, 103, 102, 80, 45, 94, 104, 104, 76, 80, 72, 73 Calculate a 95% confidence interval on the standard deviation of time until a tumor appearance using MATLAB step by step. Check the assumption of normality of the population and comment on the assumptions for the confidence interval.

Please screenshot the MATLAB

[Star Strider]

Choose the distribution carefully!

‘Check the assumption of normality of the population ...’

A normal distribution is likely not appropriate here, since that would allow for negative times to tumor appearance, implying that it would be possible for the rats to develop a tumor before being given the drug, and perhaps before they were even born. (These are possible, however it is unlikely that the experimenters would have included rats with pre-existing tumors in the experiment.)

A Poisson or lognormal distribution would be appropriate. A normal or similar distribution (with infinite support) would not.

Answer 1

[Image Analyst]

The homework problem does not state how many rats were in the test so it's unclear if there are a bunch of rats with zero or infinite times because no tumor appeared. With such a limited sample set size, it's possible that a normal distribution could have only positive numbers centered around 89, but of course if there was a huge spike at zero or infinity, that would not be Normally distributed.

However there are tests in MATLAB for normality:

h = lillietest(x) returns a test decision for the null hypothesis that the data in vector x comes from a distribution in the normal family, against the alternative that it does not come from such a distribution, using a Lilliefors test. The result h is 1 if the test rejects the null hypothesis at the 5% significance level, and 0 otherwise.

h = jbtest(x) returns a test decision for the null hypothesis that the data in vector x comes from a normal distribution with an unknown mean and variance, using the Jarque-Bera test. The alternative hypothesis is that it does not come from such a distribution. The result h is 1 if the test rejects the null hypothesis at the 5% significance level, and 0 otherwise.

h = kstest(x) returns a test decision for the null hypothesis that the data in vector x comes from a standard normal distribution, against the alternative that it does not come from such a distribution, using the one-sample Kolmogorov-Smirnov test. The result h is 1 if the test rejects the null hypothesis at the 5% significance level, or 0 otherwise.

h = adtest(x) returns a test decision for the null hypothesis that the data in vector x is from a population with a normal distribution, using theAnderson-Darling test. The alternative hypothesis is that x is not from a population with a normal distribution. The result h is 1 if the test rejects the null hypothesis at the 5% significance level, or 0 otherwise.