Consider data Set 1. In this data set, the soluble solid content of an advance selection of strawberry was investigated.  Six plants of this selection were randomly selected and soluble solid content was determined using a refractometer.  Test the hypothesis is the average soluble solid content of this selection was higher than 12.

To test the hypothesis that the average soluble solid content of the strawberry selection is higher than 12, we can follow these steps:

Step 1: State the null and alternative hypotheses:

• Null hypothesis (H0): The average soluble solid content of the selection is not higher than 12.
• Alternative hypothesis (Ha): The average soluble solid content of the selection is higher than 12.

Step 2: Choose a significance level (α):

• The significance level determines the probability of rejecting the null hypothesis when it is actually true. Let's assume a significance level of α = 0.05, which is a common choice.

Step 3: Collect and analyze the data:

• In this case, the data set includes the soluble solid content of six randomly selected plants from the strawberry selection.
• Calculate the average soluble solid content of the six plants.

Step 4: Calculate the test statistic:

• We need to calculate the test statistic to determine the likelihood of observing the obtained sample mean if the null hypothesis is true.
• The test statistic depends on the sample size, sample mean, population standard deviation (if known), and the assumed distribution of the data.
• Since the population standard deviation is not provided, we can use a t-test for small sample sizes.

Step 5: Determine the critical region:

• The critical region is the range of values that, if the test statistic falls within it, would lead to rejecting the null hypothesis.
• Since the alternative hypothesis is that the average soluble solid content is higher than 12, we are conducting a one-tailed test.
• We need to find the critical value from the t-distribution with (n-1) degrees of freedom, where n is the sample size.
• Using the significance level α = 0.05 and the degrees of freedom (n-1), we can find the critical value.

Step 6: Compare the test statistic with the critical value:

• If the test statistic falls within the critical region, we reject the null hypothesis.
• If the test statistic does not fall within the critical region, we fail to reject the null hypothesis.

Step 7: Draw a conclusion:

• Based on the comparison between the test statistic and the critical value, we can draw a conclusion about the hypothesis.
• If the test statistic falls within the critical region, we can conclude that the average soluble solid content of the strawberry selection is higher than 12.
• If the test statistic does not fall within the critical region, we cannot conclude that the average soluble solid content of the strawberry selection is higher than 12.

Please note that the specific calculations and critical values depend on the sample data and the assumed distribution.