A shadow chief secretary to the treasury claims that first-time home buyers in the South Downs area (near Worthing in Sussex, England) are paying (on average) more than £1367 in stamp duty. The shadow...

A shadow chief secretary to the treasury claims that first-time home buyers in the South Downs area (near Worthing in Sussex, England) are paying (on average) more than £1367 in stamp duty. The shadow chief secretary believes this steep tax is prohibiting families from buying a first home in this area. A random sample of first-time home buyers will be obtained, and the stamp duty paid by each family will be recorded. These data will be used to determine whether there is any evidence the mean stamp duty for firsttime home buyers, m, is more than £1367.

a. State the null and alternative hypotheses in terms of m.

b. Describe a type I error and a type II error in this context.

Recently a panel of Canadian hotel industry IT executives reported on hotel technology trends. Although 22–30% of guests shop for a room using a mobile device, only 2% actually book a room using this technology.14 Many shoppers still feel insecure completing a transaction with a credit card via a mobile device. Executives at Alt Hotels have decided to conduct a survey to determine whether hotel guests are becoming more comfortable booking a room using a mobile device. If the proportion (p = 0.02) has increased, they intend to invest more money in this technology.

 a. State the null and the alternative hypothesis.

 b. Describe a type I error and a type II error in this context.