A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are nequals189, x overbarequals7.58, sequals1.93. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 8.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

Given : Sample size

Sample mean :

Sample standard deviation :

Let be the population mean of "like" ratings of male dates made by the female dates.

As per question ,

Null hypothesis :

Alternative hypothesis : , It means the test is a one-tailed t-test. ( we use t-test when population standard deviation is unknown.)

Test statistic:

For 0.05 significance and df =188 (df=n-1) p-value = .001582. [By t-table]

Since  .001582< 0.05

Decision: p-value < significance level , that means there is statistical significance, so we reject the null hypothesis.

Conclusion : We support the claim at 5% significance that t the population mean of such ratings is less than 8.00.

38.5

step-by-step explanation:

lets say, first number = r

second number = 3r+7

total = 49

(r)+(3r+7)= 49

4r+7 = 49

4r = 42

r = 42/4

r= 10.5

3r+7 = 3(10.5)+7 = 38.5

hope this