Question

Alejandra is using a one-sample ?‑test to test the null hypothesis ?0:?=10.0 against the alternative ?1:?<10.0 using a simple random sample of size ?=15. She requires her results to be statistically significant at level ?=0.05. Determine the maximum value of ?t that will reject this null hypothesis.

You may find this table of ?t‑critical values useful. If you are using software, you may find this catalog of software guides useful.

Give your answer to three decimal places.

?=

Answer 1

Solutions The provided in formation is dis follows: Sample size na 15 significance Jevel PE 0.05 Here we wish to test the following set of bypotheses. Ho: el = 1o.o Hillclo.o This comesponds to a left tailed test for which t-test for one sample, with enknown population standard deviation will be used. To Determine the maximum value of t that will reject this could hypothesi's. ie, to find the critical t-value. eine The Aumber of degrees of Freeslom df = n1= 15-1=14, and the significance level is KOOS BEOOS Based on the provided information, the Critical t-value for a left tailed test for and .df a 14 degrees of freedom is te -1.76) +=-1.76 so we reject null hypothesis if falsalatsch <-107613 i.e. The maximum value of t that will reject the null hypothesis is t= -1-76)