Question

(CO 5) The heights of 82 roller coasters have a mean of 280.7 feet and a population standard deviation of 59.3 feet. Find the standardized tests statistics and the corresponding p-value when the claim is that roller coasters are less than 290 feet tall.

Answer 1

Solution:
Given in the question
Null hypothesis H0: = 290 feet
Alternate hypothesis Ha: < 290 feet
Number of sample(n) = 82
The sample mean (Xbar)= 280.7
Population standard deviation ()= 59.3
Here we will use the Z test as the sample size is large enough and the population standard deviation is known so standardized test statistic value can be calculated as
Z test statistic = (X-)//sqrt(n) = (280.7-290)/59.3/sqrt(82) = -1.42
So Standardized test statistic = -1.42
As this is a one-tailed test and left tailed test so from Z table we found P-value = 0.0778