Question

1. A wonderful pica restaurant in Moldova (Anton’s) reports an average of 160 grams of cheese per large pica with a standard deviation of 30 grams. Each operating site must adhere to this standard in order to be able to use the Anton name in selling their pica. Bogdan is a pica inspector. Bogdan travels the land testing pica at each Anton’s operating site. He has found that the Anton pica in Ştefan Vodă only has an average of 130 grams of cheese. Bogdan is wondering if he should rescind the rights of the Ştefan Vodă site to sell pica under the Anton brand name. What do you think?   Test at α = 0.05. Use n = 36.

Answer 1

The provided sample mean is 160 and the sample standard deviation is s = 30 , and the sample size is n = 36

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 130

The pica maintain the standard of mean 130 grams

Ha: μ ≠ 130

The pica does not maintain the standard of mean 130 grams

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is t_c = 2.03

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |t| = 6 >tc​=2.03, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0 , and since p = 0 <0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 130, at the 0.05 significance level.

Hence, The pica does not maintain the standard of mean 130 grams