Question

The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study estimated wheat prices in July and in September using independent samples of wheat producers in the two months Here are the summary statistics, in dollars per bushel Month Sample Sample Sample size mean SD 61 $3.21 $0.40 September July 80 $3.11 S0.20 The September prices are higher on the average. But we have data from only a sample of producers each month. Can we conclude that the mean wheat prices were higher in September than they were in July? Or are these differences merely what we would expect to see due to random variation? Let X = wheat prices in September and Y = wheat prices in July ux = the true population mean wheat prices in September, and wy = the true population mean wheat prices in July. Want to test the following HO: ux = uy vs. Ha: ux > wy. Find the observed t-value and P-value of the test. Select one: a the observed t-value = 251 and 2% < P-Value < 25%. b. the observed t-value = 2.12 and 1% < P-value < 2% Octhe observed t-value = 1.79 and 5% < P-value < 10% d. the observed t-value = 2.23 and 2% < P-Value < 25%. e the observed t-value = 2.51 and 0.5% < P-value < 1% Of. the observed t-value = 2.12 and 2% < P-value < 2.5%. O g. the observed t-value = 1.79 and 2.5% < P-Value < 5% Oh. the observed t-value = 2.23 and 1% < P-value < 2% i. the observed t-value = 2.05 and 2% < P-Value < 25% O j. the observed t-value = 2.05 and 2.5% < P-Value < 5%.

Answer 1

Estatistic : ze alue h - M ū, = sample mean ve 환 yo sample mean o nie na sample size 2 o? 3.21 3.11 +(0.22 61 80 6x , variance of o.1 X and Y, 0.00262 + 0.0005 observed tez te value o.1 O.L 1.79 ro.00312 0.0558 degrees of freedom (a + n₂ - 2) 61 + 80-2 = 139. P-value 0.0 756 ł 7.56%. (ع) t-value 1.79 L 5% <p-value 107