The manager of a supermarket says 50% of buyers can immediately appreciate the price of the products placed in the basket. Considering that this proportion is underestimated, a commercial consultancy makes a survey of 802 buyers, out of which 423 prove that they can really appreciate the correct price of the purchased products.

The ratio (w) of those in the sample setting the correct price is (in %, with 2 decimals): %.

Test for a threshold of 5%, 7% and 10% significance level, if you can accept the null hypothesis, that is, the director's statement that half of the buyers can appreciate the correct price.

The Critical Report (CR) is (with 2 decimals): .

The test is

At a 5% significance threshold, the z coefficient to compare the CR is (use the Excel function =NORMSINV(....) and depending on the nature of the test consider its positive and / or negative value) (write here in absolute value): . Because the CR is

At a significance threshold of 7%, the z coefficient to compare CR is (use the function Excel =NORMSINV(....) and depending on the nature of the test consider its positive and / or negative value) (write here in absolute value): . Because CR is

At a 10% significance threshold, the z coefficient to compare CR is (use the Excel function =NORMSINV(....) and depending on the nature of the test consider its positive and / or negative value) (write here in absolute value): . Because the CR is

Knowing the CR value to be established, using the =NORMSINV(....) function, which is the probability of accepting the hypothesis H0 (in %, with 2 decimals) based on this sample: %? The significance threshold (a) is in this case (in %, with 2 decimals): % and represents the probability from which the H1 hypothesis can be considered true. This level of significance is called "p-value" in English.

From the three analyzed situations, the "p-value" calculated on the basis of the sample is greater than the significance threshold of