Descriptive Statistics-One sample test of Hypothesis

Chapter 10 One ?Sample Tests of

Hypothesis

For Exercises 5-8 (a ) State the null hypothesis and the alternate hypothesis (b ) State the decision rule (c ) Compute the value of the test statistic (d ) What is your decision regarding H0 (e ) What is the p-value ? Interpret it

Alternate Hypothesis H1 : x

b ) Decision Rule : If z-0 .025 z z0 .025 , then Null Hypothesis H0 is accepted , else it is rejected

Level of significance 0 .05

c ) Here , x 59000 miles 60000 miles and 5000 miles d ) As z-0 .025 (-2

.24 z (-0 .1 z0 .025 (2 .24 , therefore , Null Hypothesis H0 is accepted i .e . the Crosset 's experience is not different from the claims made by the manufacturer

e ) p-value is 0 .9203

6 . The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed , with a mean of 3 minutes and a standard deviation of 1 minute . The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2 .75 minutes . At the .05 significance level , can we conclude that the mean waiting time is less than 3 minutes

Solution

a ) Null Hypothesis H0 : x

b ) Decision Rule : If z z-0 .025 (-2 .24 , therefore , Null Hypothesis H0 is rejected i .e . the mean waiting time is not less than 3 minutes

e ) p-value is 0 .8026

Testing for a Population Mean : Small Sample , Population

Standard Deviation Unknown

We will use the five-step hypothesis testing procedure ?n

Step 4 : Formulate the decision rule (t distribution table

18 . The management of White Industries is considering a new method of assembling its golf cart . The present method requires 42 .3 minutes , on the average , to assemble a cart . The mean assembly time for a random sample of 24 carts , using the new method , was 40 .6 minutes , and the standard deviation of the sample was 2 .7 minutes . Using the .10 level of significance , can we conclude that the assembly time using the new method is faster

Solution

Alternate Hypothesis H1 : x

Level of significance 0 .10

Here , x 40 .6 minute 42 .3 minute and s 2 .7 minute Decision rule : If t t0 .05 , 23 Null Hypothesis H0 is accepted else Alternative Hypothesis H1 is accepted

Decision : As t t0 .05 , 23 (-1 .71 , therefore , Null Hypothesis is accepted i .e . the new method is faster than the existing method

20 . Most air travelers now use e-tickets . Electronic ticketing allows passengers to not worry about a ticket , and it costs the airline companies less to handle than a ticketing . However , in recent times the airlines have received complaints from passengers regarding their e-tickets , particularly when connecting flights and a change of airlines were involved . To investigate the problem an independent watchdog agency contacted a random sample of 20 airports and collected information on the number of complaints the airport had with e-tickets for the month of March . The information is reported...