Question

Bats are nocturnal mammals, feeding on insects at night and sleeping during the day. Many species of bats use bridges as daytime sleeping places. Their choice of daytime position on the undersurface of a bridge appears to be non-random. One theory is that the bats choose locations that will keep them safer from predators. The beams that support a bridge create two kinds of spaces: wide (approximately 55 cm) and narrow (approximately 17 cm); biologists believe the narrow spaces provide more safety. Investigators studying the sleeping position choices of the Big-eared Bat (Corynorhinus rafinesquii) observed that 57 out of 102 of them were in narrow beam spaces. The narrow beam spaces accounted for approximately 46% of the available area under the bridges. The investigators want to see if this sample provides sufficient evidence that the bats prefer narrow over wide sleeping space. What is the z statistics for this test?

Answer 1

Solution:-

Given that

= x / n = 57/102 = 0.5588

P₀ = 0.57

1 - P₀ = 1-0.57 = 0.43

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.5588- 0.46 / [0.57*(0.43) /102 ]

= 2.003