Question

Braum's ker Geam store wants to decide whether to introduce a new frozen yogurt favor, They randomly selected 15 customers at their W University delve location to nate this new flusor. The rabine is on a scale of 1 to 5 , with 1 being 'rot intereated' and 5 being 'strongy interested. Bramar's will approve the new flavor if the true mean rating is aver 4 a W the vurvey stows that the average rating is 4.4 with a standard deviation of 1.6 . what is the calculated walue of the test statistic?

Answer 1

The calculated value of the test statistic for whether the true mean rating is over 4, given the sample data, is approximately 1.9365.

Step-by-step explanation:

The student is asking about how to calculate the test statistic for a sample where they want to introduce a new frozen yogurt flavor. To find the test statistic for whether the true mean rating is over 4, given an average (sample mean) rating of 4.4 with a standard deviation of 1.6 from a sample of 15 customers, we use the formula for the single-sample t-test:

Z = (\bar{x} - \mu_{0}) / (s/\sqrt{n})

Where \bar{x} is the sample mean, \mu_{0} is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values:

Z = (4.4 - 4) / (1.6 / \sqrt{15})

This gives us:

Z = (0.4) / (1.6 / \sqrt{15}) ≈ 1.9365

The calculated value of the test statistic is approximately 1.9365.