Question

Leading into Michigan's presidental primary election in 2020, a journalist, Lauren, took a random sample of 12133 university students and found that 9674 of them supported Bernie Sanders. Using this data, Lauren wants to estimate the actual proportion of university students who support Bernie Sanders. We want to use statistical inference to estimate the actual proportion of university students who support Bernie Sanders. To use a normal distribution in this scenario, which of the following conditions must be satisfied? Both n x po and n x (1-po) must be at least 10 where po is the null value for the population proportion? The observations within the sample must be independent of each other ?Any two samples must be indpendent of each other? Any two samples must be independent of eachother? There must be atleast 10 observed successes and 10 observed failures in the sample.

Answer 1

The test procedure, for one sample z-test, is appropriate to use a normal distribution when the following conditions are met:

• The sampling method for the population is simple random sampling also
• The samples are independent.
• Each sample includes at least 10 successes and 10 failures.

Thus, using the above statement the conditions that must be satisfied for using normal distribution are:

i) The observations within the sample must be independent of each other

ii) Any two samples must be independent of each other

iii) There must be atleast 10 observed successes and 10 observed failures in the sample.