QCEVault

Sampling and proportions — Question 375

Original QCE Vault practice · 5 marks

Q375 · Practice questionTechnology-activeComplex familiar5 marks

QUESTION 375 (5 marks)

A computer simulates 100100 independent samples, each containing 1010 Bernoulli trials with success probability p=0.3p=0.3. The graph shows the observed frequencies of the sample proportions. No other sample proportions occurred in this simulation.
Observed frequency column graph: sample proportions 0.1,0.2,0.3,0.4,0.5,0.6 have frequencies 13,27,32,20,6,2, respectively.
a)
How many successes occur in a sample with p^=0.3\widehat p=0.3?
[1 mark]
b)
Use the graph to estimate P(p^≥0.4)P(\widehat p\geq0.4).
[1 mark]
c)
Determine the theoretical mean and standard deviation of p^\widehat p, giving the SD to four decimal places.
[2 marks]
d)
If 10001000 samples of size 1010 were simulated, would the theoretical SD decrease? Explain.
[1 mark]
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