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1) A sample of 49 observations is taken from a normal population. The sample mean is 55 and the sample standard deviation is 10. Determine the 99% confidence interval for the population mean.

2) The Fox TV network is considering replacing one of its primetime crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.

A) Estimate the value of the population proportion.
B) Compute the standard error of the proportion.
C) Develop a 99% CI for the population proportion.
Interpret your findings.

  • Statistics -

    1) Formula using 99% confidence interval:

    CI99 = mean ± (2.58)(sd/√n)

    Note: ± 2.58 represents 99% confidence interval.

    mean = 55
    sd = 10
    n = 49

    Plug the values into the formula and calculate.

    2) Formula for 99% interval estimate of the population proportion:

    CI95 = p + or - 2.58[√(pq/n]

    p = 250/400
    q = 1 - p
    n = 400

    Convert the fractions to decimals, substitute the decimals into the formula, then finish the calculation.

    A) and B) can be answered using the information above.

    I hope this will help get you started.

  • Correction -

    For 2), the formula should read:

    CI99 = p + or - 2.58[√(pq/n)]

    Sorry for any confusion.

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