Question

A random sample of 400 families in the city of Minneapolis showed that 192 of them owned pets. The city council claims that 53% of the families in the city own pets. Does the data indicate that the actual percentage of families owning pets is different from 53%? Use a 5% significance level. For each hypothesis test please provide the following information:

(a) State the null and the alternate hypotheses.

(b) Identify the sampling distribution to be used: the standard normal distribution or the student’s t distribution. Find the critical values.

(c) Sketch the critical region and show the critical value(s) on the sketch.

(d) Compute the z or t value of the sample test statistic and show its location on the sketch of part (c).

(e) Find the P value or an interval containing the P value for the sample test statistic.

(f) Based on your answers to parts (a) through (e) decide whether to reject or not reject the null hypothesis at the given significance level. Explain your conclusion in simple non-technical terms.

Answer 1