Consider Ho: = 31 versus H₁: #31. A random sample of 36 observations taken from this population produced a sample mean of 27.70. The population is normally distributed with σ = 9. Note: Use Table IV in Appendix C to compute the probabilities. (a) Calculate the p-value. Round the answer to four decimal places. p-value= 0.0278 (b) Considering the p-value of part (a), would you reject the null hypothesis if the test were made at the significance level of 0.05? the null hypothesis. Reject (c) Considering the p-value of part (a), would you reject the null hypothesis if the test were made at the significance level of 0.01? Do not reject ✓the null hypothesis.

A standardized math test of fifth grade students produces a mean ?μ = 100 with a ?σ = 18. A sample of n = 36 students participated in "boost" training for their math skills. The sample M = 104 with S = 24.  Did this "boost" training significantly improve students' math performance? Use ?α = .01.

A given distribution has a population mean, μ, of 142 and a population standard deviation, σ, of 10.  What z-score would be associated with the value x = 110?

A given distribution has a population mean, μ, of 142 and a population standard deviation, σ, of 12.  What z-score would be associated with the value x = 146?

A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. Use μ1 for the mean number of families with no children. At α=0.01 , is there a difference between the means? Use the P -value method and tables.   X σ n No children 8.6 2.6 22 Children 10.1 2.7 22 (a) State the hypothesis and identify the claim with the correct hypothesis. H0:  ▼(Choose one) H1:  ▼(Choose one) This hypothesis test is a ▼(Choose one) test.       (b)Find the critical value(s). Round the answer to 3decimal places, if necessary. If there ismore than one critical value,   Critical values:   (c)Compute the test value. Round the answer to at least 3 decimal places, if necessary. z= Compute the P -value. Round the answer to four…

The random sample of n=75�=75 yielded a sample mean of x¯=26�¯=26.Assume that we know the population standard deviation is σ=30�=30.    Step 2 of 3 :   Calculate a 95% confidence interval for the population mean. Round your answers to 2 decimals places.

Is the difference between the mean annual salaries of registered nurses in State A and State B equal to ​$11,000​? To​ decide, you select a random sample of registered nurses from each state. The results of each survey are shown. Assume the population standard deviations are σ1=​$8350 and σ2=​$7624. At α=0.01​, what can you​ conclude?   Registered Nurses in State A Registered Nurses in State B x1 = 75,876 n1 = 30 x2 = 70,876 n2 = 25

A given distribution has a population mean, μ, of 143 and a population standard deviation, σ, of 6.  What z-score would be associated with the value x = 112?

A given distribution has a population mean, μ, of 116 and a population standard deviation, σ, of 11.  What z-score would be associated with the value x = 158?

A given distribution has a population mean, μ, of 138 and a population standard deviation, σ, of 9.  What z-score would be associated with the value x = 142?