For each of the following claims Mention what kind of test s

For each of the following claims: Mention what kind of test should be used (one-tail, two-tail) and set up the null and alternate hypothesis. Consider that the critical value is = CV (value retrieved from z or t table). For each H0, mentioned the acceptance range. a. The Pastry shop claims that its chocolate cookies have at least 80%chocolate per cookie. b. The 87Cents Store claims that their daily profit is at most $2000. c. The meat store claims that their pre-packed hot-dogs weight .5 pound.

Solution

The Pastry shop claims that its chocolate cookies have at least 80%chocolate per cookie.

Mention what kind of test should be used.

The test is one tailed (right tail).

Here we are testing the proportion.

The hypothesis for the test is,

H0 : p = 80% = 0.80 Vs H1 : p > 80% = 0.80

Consider that the critical value :

Assume that alpha = level of significance = 0.05

Critical value we can find by using EXCEL.

=NORMSINV(probabiliity)

where probability = 1 - alpha

critical value = 1.645

If calculated Z > critical value

Reject H0 at 5% level of significance.

and if calculated Z < critical value

Accept H0 at 5% level of significance.

b) The 87Cents Store claims that their daily profit is at most $2000.

The test is one tailed.

The hypothesis for the test is,

H0 : mu = $2000 Vs H1 : mu < $2000

where mu is population mean.

Here we use t-test.

This is the testing for population mean.

The critical value is in EXCEL is,

tinv(probability, deg_freedom)

probability = 0.05

deg_freedom = 87 - 1 = 86

critical value = 1.9879

If calculated t > critical value

Reject H0 at 5% level of significance.

and if calculated t < critical value

Accept H0 at 5% level of significance.

c. The meat store claims that their pre-packed hot-dogs weight .5 pound.

The test is two tailed.

The hypothesis for the test is,

H0 : mu = 0.5 pound Vs H1 : mu 0.5 pound

Assume that alpha (a)= level of significance = 0.05

Consider that the critical value (CV) in EXCEL is,

=NORMSINV(probability)

where probability = 1 - a/2 = 0.975

critical value = 1.96

If calculated Z > critical value

Reject H0 at 5% level of significance.

and if calculated Z < critical value

Accept H0 at 5% level of significance.