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A survey was conducted to estimate the mean number of books (denoted by µ) each university...

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Statistics

A survey was conducted to estimate the mean number of books(denoted by µ) each university student read in the last year. Amonga random sample of 51 students, the number of books each studentread in the last year was recorded. The sample mean was 8.039 andthe sample standard deviation was 2.545.

a. Write down the point estimate of µ.

b. Calculate the standard error of the point estimate in a.

c. To construct a 95% two-sided confidence interval for µ,what’s the multiplier to use?

d. Calculate the lower endpoint of the 95% two-sided confidenceinterval for µ.

e. Calculate the upper endpoint of the 95% two-sided confidenceinterval for µ.

f. Consider a hypothesis testing problem where the nullhypothesis is H0 : µ = 10 and the alternative hypothesis is Ha : µ6= 10. Use a significance level of 0.05. Based on the 95% two-sidedconfidence interval for µ above, what’s your decision about whetherto reject H0? Give a brief explanation.

g. Suppose you’re asked to conduct a hypothesis testing to showthat on average a student read more than 5 books last year. Whichpair of hypotheses should be used? (5 points) A. H0 : µ = 5 againstHa : µ 6= 5 B. H0 : µ < 5 against Ha : µ ≥ 5 C. H0 : µ ≤ 5against Ha : µ > 5 D. H0 : µ ≥ 5 against Ha : µ < 5

Answer & Explanation Solved by verified expert
3.8 Ratings (430 Votes)
a The point estimate of mean of a populationis equal to the sample meanHencePoint Estimate ofb The standard error of point estimate of iSince the standard deviation of the population is not knownhence instead of the standard deviation of the population we woulduse sample standard deviation to calculate the standard errorHenceThe standard error of point estimate    See Answer
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