Question

# There is a beautiful hill station in India called ‘Kurseong’. Besides breathtaking views, this town is...

There is a beautiful hill station in India called ‘Kurseong’. Besides breathtaking views, this town is also famous for its locally made spicy pickle called Tittira. A random group of 60 tourists from different parts of the world was asked to taste Tittira and using the data, the estimated standard error of the sample proportion of tourists who liked Tittira is calculated as 0.0632.

A normal distribution can be used to model the sampling distribution of the sample proportion. The pickle salespeople constructed a confidence interval for the actual proportion of tourists who like Tittira.

Following that, they collect a new sample of size 100 and find that the sample proportion is the same as the first sample proportion.

Consider the statement:

The estimated standard error for the sample proportion based on the new sample is less than the first sample's standard error.

Is this statement always true or sometimes true or never true?

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