To test the hypothesis, we can use the t-test. The formula for the t-statistic is:
t = (x̄ - μ) / (s / sqrt(n))
Where:
x̄ is the sample mean (2.5 grams)
μ is the population mean (2.4 grams)
s is the sample standard deviation (0.3 grams)
n is the sample size (15 oranges)
Plugging in the given values, we get:
t = (2.5 - 2.4) / (0.3 / sqrt(15))
t = 0.1 / (0.3 / sqrt(15))
t ≈ 0.661
To determine the outcome of the test, we need to compare the test statistic (0.661) to the critical value. Since the significance level is 1%, we are using a two-tailed test.
The critical value for a two-tailed test with a significance level of 1% and 14 degrees of freedom (15 - 1 = 14) is approximately ±2.977.
Since 0.661 falls within the range of -2.977 to +2.977, we fail to reject the null hypothesis (H0). There is not enough evidence to conclude that the mean sugar content per orange shipped from the particular grove is different from 2.4 grams at a 1% significance level.
A buyer wants to determine whether the mean sugar content per orange shipped from a particular grove is 2.4 grams. A random sample of 15 oranges produced a mean sugar content of 2.5 grams and a standard deviation of 0.3 grams. Test H0: μ = 2.4 against Ha: μ ≠ 2.4 using a 1% significance level. Calculate the test statistic and give the outcome of the test.
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