A convenience store owner believes that the median number of lottery tickets sold per day is 49. A random sample of 20 days yields the data below. Find the critical value to test the owner's claim.



32 48 59 64 31 55 70 27 33 38
47 54 54 44 44 49 49 59 54 38

To find the critical value for testing the owner's claim, we need to perform a hypothesis test and determine the level of significance or alpha value.

Let's assume that the null hypothesis is "the median number of lottery tickets sold per day is indeed 49," and the alternative hypothesis is "the median number of lottery tickets sold per day is different from 49."

Given that the sample size is less than 30, we will use the Wilcoxon signed-rank test to test the owner's claim.

Since we have 20 observations, we need to calculate the one-sided critical value at a chosen alpha level.

To find the critical value, we can refer to the Wilcoxon signed-rank table or use software for calculations. Since we don't have the table handy, let's use software.

Assuming a two-sided test (since the alternative hypothesis is two-sided), we can use statistical software or online calculators to find the critical value. Let's use an online calculator.

Entering the given data into an online calculator or software program will yield the critical z-value.

Note: As an AI text-based bot, I am unable to perform real-time calculations or use online calculators. However, you can use statistical software or search for an online calculator to find the critical value for the Wilcoxon signed-rank test using the given dataset.

By comparing the calculated z-value with the appropriate critical value, we can determine whether to reject or fail to reject the null hypothesis.

To find the critical value to test the owner's claim, we need to perform a hypothesis test using the data provided. In this case, the owner claims that the median number of lottery tickets sold per day is 49.

Here are the steps to conduct the hypothesis test:

Step 1: State the null and alternative hypotheses:
The null hypothesis (H0) is that the median number of lottery tickets sold per day is equal to 49.
The alternative hypothesis (Ha) is that the median number of lottery tickets sold per day is not equal to 49.

Step 2: Determine the level of significance (α):
The level of significance is a predetermined threshold to determine if there is enough evidence to reject the null hypothesis. Let's assume a significance level of 0.05 (or 5%).

Step 3: Calculate the test statistic:
In this case, since the sample size is less than 30, we will use the sign test. The sign test compares the observed values against the hypothesized median. We count the number of times the observed values are greater than the hypothesized median and compare it to the binomial distribution. However, we need to arrange the data in ascending order first:

27 31 32 33 38 38 44 44 47 48
49 49 54 54 54 55 59 59 64 70

We observe that there are 5 values less than the hypothesized median (49). Therefore, the test statistic is 5.

Step 4: Determine the critical value:
Since we are using a two-tailed test because the alternative hypothesis is not equal to 49, we need to find the critical value for an alpha level of 0.05 and a sample size of 20.

To find the critical value, you can use a statistical table called the binomial distribution table or use statistical software. The critical value is the number of successes needed in a binomial distribution given the sample size and significance level.

Using software or consulting a binomial distribution table, you can find that for an alpha level of 0.05 and a sample size of 20, the critical value is 4.

Therefore, the critical value to test the owner's claim is 4.