Given a sample size of 18, with sample mean 660.3 and sample standard deviation
95.9, we are to perform the following hypothesis testing:
Null Hypothesis H0 : µ = 700
Research Hypothesis H1 : µ ≠ 700
•What is the test statistics?
•At a 0.05 significance level, what is the critical value in this test? Do we reject the null hypothesis?
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To perform this hypothesis test, we need to calculate the test statistic and compare it to the critical value at a given significance level.
The test statistic we use for this scenario is the z-score. The formula to calculate the z-score is:
z = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is 660.3, the population mean is 700, the sample standard deviation is 95.9, and the sample size is 18. Plugging in these values into the formula, we get:
z = (660.3 - 700) / (95.9 / sqrt(18))
Calculating this expression will give us the test statistic value.
To find the critical value, we need to look up the z-value associated with the chosen significance level using the z-table. For a two-tailed test at a 0.05 significance level, we divide the significance level by 2 (0.05/2 = 0.025) and find the z-score that corresponds to the area of 0.025 in both tails of the standard normal distribution. This z-score will serve as the critical value.
Once we have the z-score test statistic and the critical value, we can compare them to make a decision. If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Please provide the z-values calculated and the critical value at a 0.05 significance level, so that I can help you determine whether to reject the null hypothesis.