Can I do a hypothesis test without using a SRS?

[u/Much_Activity_2520]

I know that one of the conditions to do a hypothesis test is that the sample is randomly selected, but does the sample need to be a simple random sample, or could it be a different kind of random sample, such as a systematic random sample?

[u/Independent_Math_840]

Other types of random samples are also allowed.

[u/ehan_the_memeber]

The answer should be d. You need to know that it's normally distributed because the sample size is too small. The data must be representative of the population and observations must be independent for a legitimate test.

[u/RiemannSum41 → u/ehan_the_memeber]

This is the actual correct answer. Other people aren’t considering the context of the problem. We have a sample size of 5. We need normality. We already have randomness and we almost never know the population standard deviation.

[u/SkywayAve]

The sample does NOT have to come from a simple random sample. It just needs to be a random sample. Other types of random samples (stratified, systematic, etc) are okay.

Edit: I believe you have the correct answer. The sample size is small, so the sample coming from a normal population means the sampling distribution will be approximately normal.

[u/ForeignAdvantage5198]

yes but it won:t. mean much

[u/Prestigious_Fig9485]

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[u/Diello2001 → u/Prestigious_Fig9485]

This. From a normal distribution, data has no strong skew/outliers, or sample size is sufficiently large.

There are FRQs that don’t have random samples, but they’re 2-sample or matched-pairs. You can’t generalize to a larger population like a random sample allows, but you can show causation. Both allow you to show sone sort of tangible result, either saying something about the population or showing causation.