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Probability Alpha or Level of Significance Problem

Probability Alpha or Level of Significance Problem

Question Description

I need support with this Excel question so I can learn better.

PROBLEMS:

If alpha is not provided, use 0.05 level of significance.

Problem 1 (15 points)

The daily return of a certain stock is normally distributed with a mean of 0.20% and a standard deviation of 2.50%.

a. Find the probability that the return on a randomly selected day is negative.

State the Excel function (specifying all inputs) that will compute this probability.

b. Find the level, L, such that there is a 15% chance that the daily return on a randomly selected day exceeds L.

State the Excel function (specifying all inputs) that will compute L.

c. Find the probability that the average return over 4 randomly selected days is negative?

State the Excel function (specifying all inputs) that will compute this probability.

d. Find the probability that the return is negative on each of 4 randomly selected days? (Joint probability)

e. Find the level, M, such that there is a 30% chance that the average return over 4 randomly selected days exceeds M.

State the Excel function (specifying all inputs) that will compute M.

Problem 2 (12 points)

SmithCo is a supplier to many brand name makers of mobile phones. SmithCo manufactures the external shells that enclose mobile phones. The strength of a shell is measured by applying increasing pressure to the shell and recording the pressure at which the shell breaks. Shell strengths are approximately normally distributed. A random sample of 12 shells made by SmithCo showed an average strength of 45.0 pounds and a standard deviation of 2.0 pounds. We wish to construct a 90% confidence interval for the mean shell strength.

a. State the appropriate z-value or t-value that must be used.

b. State the confidence interval in the form a ± b.

c. State the confidence interval in the form [c, d].

d. Determine the sample size required to estimate the mean strength within one pound with a 95% confidence level and assuming that the population standard deviation is 2 pounds.

Problem 3 (23 points)

A marketing company reported that the typical American spends a mean of 150 minutes per day accessing the Internet via a mobile device. In order to test the validity of this statement, you select a random sample of 30 individuals. The results for the time spent per day accessing the Internet via mobile device (in minutes) are stored in Times.xlsxPreview the document. Is there evidence that the population mean time spent per day accessing the Internet via mobile device is greater than 150 minutes?

a. Specify the null hypothesis and the alternative hypothesis. (4 points)

b. State whether the test is a lower-, upper-, or two-tailed test and explain your reasoning.

c. State the appropriate z-value or t-value that must be used and the rejection region.

d. Calculate the test statistic.

e. Provide the p-value for the test statistic.

f. Determine the statistical decision.

g. Communicate the results of the test in “plain English” within the context of the problem. (4 points)


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