statistics

Consider the following hypotheses:

H0: μ = 120

HA: μ ≠ 120

The population is normally distributed with a population standard deviation of 46. Use Table 1.

a.

Use a 5% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

  Critical value(s) ±   

b-1.

Calculate the value of the test statistic with  = 132 and n = 50. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

  Test statistic   

b-2. What is the conclusion at α = 0.05?       Reject H0 since the value of the test statistic is greater than the critical value. Reject H0 since the value of the test statistic is smaller than the critical value. Do not reject H0 since the value of the test statistic is greater than the critical value. Do not reject H0 since the value of the test statistic is smaller than the critical value.

c.

Use a 10% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

  Critical value(s) ±   

d-1.

Calculate the value of the test statistic with  = 108 and n = 50. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

  Test statistic   

d-2. What is the conclusion at α = 0.10?       Reject H0 since the value of the test statistic is not less than the negative critical value. Reject H0 since the value of the test statistic is less than the negative critical value. Do not reject H0 since the value of the test statistic is not less than the negative critical value. Do not reject H0 since the value of the test statistic is less than the negative critical value.  6.      

In order to conduct a hypothesis test of the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 4.8 and 0.8, respectively. Use Table 2.

Use the p-value approach to conduct the following tests at α = 0.05.

H0: μ ≤ 4.5 against HA: μ > 4.5

a-1.

Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your answer to 2 decimal places.)

  Test statistic   

a-2.

Approximate the p-value.

      0.05 < p-value < 0.10 0.005 < p-value < 0.01 0.025 < p-value < 0.05

a-3.

What is the conclusion?

      Reject H0 since the p-value is less than α. Reject H0 since the p-value is greater than α. Do not reject H0 since the p-value is less than α. Do not reject H0 since the p-value is greater than α.

H0: μ = 4.5 against HA: μ ≠ 4.5

b-1.

Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your answer to 2 decimal places.)

  Test statistic   

b-2.

Approximate the p-value.

      0.05 < p-value < 0.10 0.025 < p-value < 0.05 0.005 < p-value < 0.01

b-3.

What is the conclusion?

      Reject H0 since the p-value is less than α. Reject H0 since the p-value is greater than α. Do not reject H0 since the p-value is less than α. Do not reject H0 since the p-value is greater than α.

In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. Compute 90% and 99% confidence intervals for the population mean 30-year fixed mortgage rate. Use Table 1.(Round intermediate calculations to 4 decimal places, "z" value and final answers to 2 decimal places. Enter your answers as percentages, not decimals.)

Confidence Level Confidence Interval 90%  %  to  %  99%  %  to  %  8.      

An article in the National Geographic News (“U.S. Racking Up Huge Sleep Debt,” February 24, 2005) argues that Americans are increasingly skimping on their sleep. A researcher in a small Midwestern town wants to estimate the mean weekday sleep time of its adult residents. He takes a random sample of 80 adult residents and records their weekday mean sleep time as 6.4 hours. Assume that the population standard deviation is fairly stable at 1.8 hours. Use Table 1.

a.

Calculate a 95% confidence interval for the population mean weekday sleep time of all adult residents of this Midwestern town. (Round intermediate calculations to 4 decimal places, "z" value and final answers to 2 decimal places.)

  Confidence interval to   

b.

Can we conclude with 95% confidence that the mean sleep time of all adult residents in this Midwestern town is not 7 hours?

      Yes, since the confidence interval contains the value 7. Yes, since the confidence interval does not contain the value 7. No, since the confidence interval contains the value 7. No, since the confidence interval does not contain the value 7.  9.      

A random sample of 24 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 104.6 and 28.8, respectively. Assume that the population is normally distributed. Use Table 2.

a.

Construct a 90% confidence interval for the population mean. (Round intermediate calculations to 4 decimal places, "t" value to 3 decimal places, and final answers to 2 decimal places.)

  Confidence interval    to   

b.

Construct a 99% confidence interval for the population mean. (Round intermediate calculations to 4 decimal places, "t" value to 3 d 

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The MorTex Company Sum Solution

The MorTex Company assembles garments entirely by hand even though a textile machine exists that can assemble garments faster than a human can. Workers cost $50 per day, and each additional laborer can produce 200 more units per day (i.e., marginal product is constant and equal to 200). Installation of the first textile machine on the assembly line will increase output by 1,800 units daily. Currently the firm assembles 5,400 units per day.

The financial analysis department at MorTex estimates that the price of a textile machine is $600 per day. Can management reduce the cost of assembling 5,400 units per day by purchasing a textile machine and using less labor? Why or why not? The Textile Workers of America is planning to strike for higher wages. Management predicts that if the strike is successful, the cost of labor will increase to $100 per day. If the strike is successful, how would this affect the decision in part a to purchase a textile machine? Explain. 

 

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