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Statistics and Probability

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Variance Hypothesis Test

STATS-L4KVZ4

Suppose two independent random samples of sizes ${ n }_{ 1 }=5$ and ${ n }_{ 2 }=16$ have been taken from two normally distributed populations of waiting times at a grocery ATM (1) and a bank ATM (2) and the sample standard deviations are $s_{1} = 5$ and $s_{2} = 9.$

If you test:

$${ H }_{ 0 }:{ \sigma }_{ 1 }^{ 2 }={ \sigma }_{ 2 }^{ 2 } { H }_{ 1 }:{ \sigma }_{ 1 }^{ 2 }\neq { \sigma }_{ 2 }^{ 2 }$$

...with alpha = 0.05, what would you conclude?

Use alpha = 0.05 and an F_table: http://www.pindling.org/Math/Statistics/Textbook/Functions/FDist/FDist_025.htm

A

Both ATMs have the same waiting time.

B

The waiting time at the grocery is more variable than at the bank.

C

There is no evidence that the waiting times differ in variability.

D

The waiting time at the bank is more variable than at the grocery.