Question

Use the following information to answer questions 25-31 A traveler wants to know if the prices of hotels are different. She samples 10 cities and finds the prices below. Use a paired-sample t-test to determine whether the difference between hotel prices is significant at the a 0.01 confidence level Cities Atlanta Boston Chicago Dallas Denver Indianapolis Los Angeles New York City 517 Philadelphia Washington, DC 251 Hyatt Regency prices in dollars Hilton prices in dollars 90 273 204 303 189 269 133 418 206 225 211 274 607 172 172 144 25) Find the sample mean of the difference between hotel prices, : 26) Find the sample standard deviation of the difference between hotel prices, s 27) Find the value of the test statistic 28) What type of test will you use (left-tailed, right-tailed, or two-tailed)? 29) What is the degrees of freedom of the test, v? 30) Using a calculator or table, determine whether the p-value is greater or less than and state your decision about the null hypothesis. a 0.01 31) Find the 99% confidence interval of the difference between means.

Answer 1

25)

Sample mean of difference = -26.80

26)

Sample std.dev of difference= 81.1402

27)

test statistics:

t = xbar / (sd/sqrt9n))
= -26.80/(81.1402/sqrt(10))
= -1.044

28)

two tailed

Hypothesis are as:

H0 : mud = 0
Ha: mud not =0

29)

df = 10 - 1 = 9

30)

p value = 2 *P(t < -1.044) with df = 9

= 2* 0.1618

P value= 0.3236

As p value > 0.01 Fail to reject H0

31)

t value at 99% = 3.250

CI = xbar +/- t (sd/sqrt(n))
= -26.80 +/ - 3.250 * (81.1402/sqrt(10))

= (-110.1868 , 56.5868 )

The 99% Ci is (-110.1868 , 56.5868 )