A club spins a four-color spinner 100 times. The table shows the observed counts by color and the counts expected for a fair spinner. What is the chi-squared statistic, rounded to the nearest hundredth?

A cafeteria claims entree choices are 40% pizza, 30% tacos, 20% salad, and 10% pasta. The table gives the observed and expected counts for 200 lunches. What is chi-squared?

A clinic claims appointments are evenly spread over five weekdays. In 150 appointments, the table shows the observed count and expected count for each weekday. What is the chi-squared statistic?

A factory claims package colors are 50% white, 25% blue, 15% green, and 10% gray. The table gives the observed and expected counts for 200 packages. Find chi-squared.

A school survey claims music preferences are 30% pop, 30% hip-hop, 20% country, and 20% rock. The table gives the observed and expected counts for 250 responses. Find chi-squared.

A biology class expects moth colors in a 9:3:3:1 ratio among 160 moths. The table gives the observed and expected counts. What is the chi-squared statistic?

A cookie shop claims customer flavor choices are 35% chocolate, 25% sugar, 25% oatmeal, and 15% peanut butter. A goodness-of-fit test is run on one week's observed counts. What are the null and alternative hypotheses?

A transit office claims bus arrivals are 10%, 20%, 30%, and 40% across four time blocks. A goodness-of-fit test uses one month of counts. What hypotheses should be tested?

A park guide claims bird sightings are 40% sparrow, 25% robin, 20% finch, and 15% wren. A class records sightings and runs a goodness-of-fit test. What are the correct hypotheses?

A cereal company claims prize colors are equally likely among five colors. A store checks boxes with a goodness-of-fit test. What are the appropriate hypotheses?

A bookstore tests whether 120 sales match a claimed distribution across five fixed genres. No distribution parameter is estimated from the sample. What degrees of freedom should be used for the chi-squared goodness-of-fit test?

A blood drive compares the observed blood types of 200 donors with claimed percentages for four blood-type categories. What degrees of freedom does the chi-squared goodness-of-fit test use?

A game club rolls a die 60 times to test the claimed distribution across six faces. For the chi-squared goodness-of-fit test, how many degrees of freedom are used?

A genetics lab tests a claimed plant phenotype ratio using 160 plants in four phenotype categories. What degrees of freedom should be used for the chi-squared goodness-of-fit test?

A seed company claims a $9:3:3:1$ plant phenotype ratio. A goodness-of-fit test on 160 plants reports ${\chi }^2=9.41$, df = 3, and p-value 0.024. At $\alpha =0.05$, what conclusion follows?

A streaming service claims fixed listening shares for four music genres. A goodness-of-fit test from 500 plays gives ${\chi }^2=4.89$, df = 3, and p-value 0.180. At $\alpha =0.05$, what is the conclusion?

A manufacturer claims defect types follow its historical percentages. A goodness-of-fit test on this month's defects reports ${\chi }^2=12.45$, df = 3, and p-value 0.006. At $\alpha =0.01$, what should be concluded?

A zoo claims animal births are evenly distributed across four seasons. A goodness-of-fit test gives ${\chi }^2=6.98$, df = 3, and p-value 0.072. At $\alpha =0.10$, what conclusion is appropriate?

A school club claims membership is 25% from each grade. A goodness-of-fit test using current members reports ${\chi }^2=8.25$, df = 3, and p-value 0.041. At $\alpha =0.01$, what conclusion follows?

A hospital claims patient blood-type percentages match regional rates. A goodness-of-fit test on 300 patients reports ${\chi }^2=3.65$, df = 3, and p-value 0.300. At $\alpha =0.05$, what is the conclusion?