Question

escape the rooms have been quite popular recently. people pay to get locked in a room where they have to piece together clues to escape in 60 minutes. in Worcester the population mean time to escape the museum room was 42 minutes , so they decided to make the room more challenging. after modifications, a sample of 14 groups had a mean escape time of 50 minutes and a sample standard deviation of 11 minutes . assume that the escape times are normally distributed. perform a hypothesis test at 1% significance level using the critical-value approach to determine if there is sufficient evidence that the modifications increased the escape time. show all steps and draw and label a picture of rejection region.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 42

H_a :    42

Test statistic = t

= ( - ) / s / n

= (50 - 42) / 11 / 14

= 2.721

Test statistic = 2.721

n = 14

df = 14 - 1 = 13

t _/2,df = t_0.005,13 = 3.012

Test statistic < critical value

Fail to reject the null hypothesis .

There is not sufficient evidence that the modifications increased the escape time .