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5 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2022 · Paper 2 · Question 5(b)

A scientist collected a random sample of 100 measurements from a normal population with a mean of 500 and a standard deviation of 80. Determine the probability that the scientist will get a sample mean within the values 490 and 510, inclusively.

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Other parts of this question

  1. 5(a)(i)State ONE reason why the population proportion, p, cannot be stated as 35%, although the sample size is large.[1 mark]
  2. 5(a)(ii)Determine if the required conditions for the construction of a confidence interval for p are satisfied.[2 marks]
  3. 5(a)(iii)Identify the sampling distribution of p-hat. You must state the specific parameters of the sampling distribution.[3 marks]
  4. 5(a)(iv)Construct a two-sided 90% confidence interval for p.[4 marks]
  5. 5(a)(v)Interpret the obtained confidence interval in the context of the problem.[2 marks]
  6. 5(a)(vi)aTest the null hypothesis H_0 : p = 0.40 against the alternative H_1 : p > 0.40 at the significance level of alpha = 0.05: Calculate the test statistics.[4 marks]
  7. 5(a)(vi)bDetermine the critical value.[1 mark]
  8. 5(a)(vi)cDetermine the critical region.[1 mark]
  9. 5(a)(vi)dState a valid conclusion for the test. Give ONE reason for the conclusion stated.[2 marks]

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